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Research

Summary 


My fields of research are mathematical physics and applied mathematics. In particular, I have been actively involved in the theory of integrable systems, the field of othogonal polynomials, and special functions theory. Recently, we have proven a spectral theorem à la Favard for bounded banded operators, extending the well known spectral Favard theorem for Jacobi matrices. I have also conducted investigations on random walks and Markov chains beyond birth and death. Other research interests include the application of the Riemann—Hilbert problem in characterizing non-Abelian Painlevé discrete equations and the use of the Gauss—Borel factorization of semi-infinite Gram matrices to discover Christoffel and Geronimus formulas in various extended orthogonalities. I have studied orthogonalities in the following forms: discrete, matrix, multivariate, mixed multiple, and Sobolev. The relationship between new integrable systems or families of solutions and these orthogonal systems has also been a significant focus of my studies.

I have coauthored 135 scientific publications, 103 of which are published in JCR journals (including 61 in Q1, with 25 beyond percentile 90). My work has been featured in renowned scientific journals such as Advances in Mathematics (5), Inverse Problems (3), Communications in Mathematical Physics, International Mathematics Research Notices, Journal of Nonlinear Sciences, Bulletin of Mathematical Sciences, Studies in Applied Mathematics (5), Journal of Computational and Applied Mathematics, Analysis and Mathematical Physics (4), Publications of the Research Institute of Mathematical Sciences, Journal of Mathematical Analysis and Applications (3), Linear Algebra and its Applications (4), Proceedings of the American Mathematical Society (3), Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (2), Letters in Mathematical Physics, Physica D: Nonlinear Phenomena (3), Physics Letters B (8), and Journal of Physics A (20). Additionally, I have acted as a reviewer for over 40 scientific JCR journals, including Applied Mathematics and Computation,  Annales Henri Poincaré, Inverse Problems, Journal of Approximation Theory, Nonlinearity, Proceedings of the Royal Society, Studies in Applied Mathematics, Journal of Computational and Applied Mathematics, Journal of Mathematical Analysis and Applications, Linear Algebra and its Applications, Nuclear Physics B, Physica D, Journal of Physics A, Physica Scripta and The European Journal of Physics Plus. Furthermore, I have assisted CRC Press (Taylor & Francis) in assessing scientific book proposals.

Presently, I am leading a Spanish National Plan project, and I have also led two other Spanish National Plan projects, all within the field of Mathematics. I have been a research member of six international research projects and ten Spanish research projects. I have contributed a total of 45 presentations at international research congresses and delivered 34 research seminars at various universities. I have served as a visiting professor at the following institutions: Johannes Kepler Linz University (Austria), University of Aveiro (Portugal), University of California at Berkeley (USA), Tsinghua University (Beijing, China), China University of Mining and Technology (Beijing, China), Université Catholique de Louvain (Belgium), SISSA-International School for Advanced Studies in Trieste (Italy), Isaac Newton Institute of the Cambridge University (United Kingdom), La Sapienza, Universitá di Roma (Italy), and Leeds University (United Kingdom). I have supervised three PhD theses and I am currently supervising two more. Additionally, I have organized R&D&I activities, including international scientific conferences. I have evaluated scientific proposals for institutions such as Agencia Estatal de Investigación (Spain), NWO (the Netherlands), European Science Foundation, FWO (Flanders, Belgium), FONDECYT (Chile), Agencia Andaluza del Conocimiento (Spain), and the Banff International Research Station. 


Research Projects as Team Leader

  • PID2021-122154NB-I00, Ortogonalidad y aproximación con aplicaciones en machine learning y teoría de la probabilidad (2022-24). Budget: 104.000 €. Research leaders (IPs): David Gómez-Ullate and  Manuel Mañas Baena,  team of 6 researchers.
  • PGC2018-096504-B-C33, Ortogonalidad y aproximación: Teoría y aplicaciones en física matemática (2019-21). Budget: 42.108 €. Research leaders (IPs): Francisco Marcellán Español and  Manuel Mañas Baena, team of  8 researchers.
  • MTM2015-65888-C4-3-P, Ortogonalidad, teoría de la aproximación y aplicaciones en física matemática (2016-19). Budget: 30.613 €. Research leaders (IPs): Manuel Mañas Baena and David Gómez-Ullate, team of  3 researchers.

Publications

JCR papers

  1. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Finite Markov chains and multiple orthogonal polynomials. Journal of Computational and Applied Mathematics (2024). JIF percentile: 83.3. Accepted.
  2. Gerardo Ariznabarreta, Juan Carlos García-Ardila, Manuel Mañas, and Francisco Marcellán. Uvarov Perturbations for Matrix Orthogonal Polynomials. Proceedings of the American Mathematical Society B11 (2024), 525-537. doi:10.1090/bproc/235. JIF percentile: 63.7.
  3. Gerardo Ariznabarreta, Manuel Mañas, and Piergiulio Tempesta. Generalized Sobolev orthogonal polynomials, Gauss-Borel factorization and perturbations. Analysis and Mathematical Physics 14, article number 89 (2024). doi:10.1007/s13324-024-00883-5.JIF percentile: 88.4.
  4. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Hypergeometric Expressions for Type I Jacobi-Piñeiro Orthogonal Polynomials with Arbitrary Number of Weights. Proceedings of the American Mathematical Society  B11 (2024)  200–210. doi:10.1090/bproc/225. JIF percentile: 63.7..
  5. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Bidiagonal factorization of the recurrence matrix for the multiple Hahn orthogonal polynomials, Linear Algebra and its Applications (2024). doi:10.1016/j.laa.2024.03.033. JIF percentile: 76.2.
  6. Itsaso Fernández-Irisarri and Manuel Mañas. Toda and Laguerre-Freud equations  and tau -functions for hypergeometric discrete multiple orthogonal polynomials. Analysis and Mathematical Physics 14 (2024), article number 30. doi:10.1007/s13324-024-00876-4.  JIF percentile: 88.4.
  7. Itsaso Fernández-Irisarri and Manuel Mañas. Matrix Factorizations for the Generalized Charlier and  Meixner Orthogonal Polynomials. Linear Algebra and its Applications (2024) doi:10.1016/j.laa.2024.01.012. JIF percentile: 76.2.
  8. Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi, and Manuel Mañas. Matrix Jacobi Biorthogonal Polynomials via Riemann-Hilbert problem. Proceedings of the American Mathematical Society 152 (2024), 193–208. doi:10.1090/proc/16431.  JIF percentile: 63.7.
  9. Amilcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, Manuel Mañas, and Carlos Álvarez-Fernández, Jacobi-Piñeiro Random Walks. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 118 (2024), article number 15. doi:10.1007/s13398-023-01510-x. JIF percentile: 92.1.


    2023


  10. Itsaso Fernández-Irisarri and Manuel Mañas, Laguerre-Freud equations for the Gauss hypergeometric discrete orthogonal polynomials. Mathematics 11 (2023), 4866. doi:10.3390/math11234866. JIF percentile: 95.8
  11. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials. Advances in Mathematics 434 (2023), 109313. doi:10.1016/j.aim.2023.109313. JIF percentile: 89.5.
  12. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Positive bidiagonal factorization of tetradiagonal Hessenberg matrices. Linear Algebra and its Applications 667 (2023), 132-160. doi:10.1016/j.laa.2023.08.001. JIF percentile: 76.2.
  13. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Oscillatory banded Hessenberg matrices, multiple orthogonal polynomials and random walks. Physica Scripta 98 (2023), 105223. doi:10.1088/1402-4896/ace93d. JIF percentile: 67.7.
  14. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Hahn multiple orthogonal polynomials of type I: Hypergeometric expressions. Journal of Mathematical Analysis and Applications 528 (2023), 1277471.doi:10.1016/j.jmaa.2023.127471. JIF percentile: 83.7.
  15. Itsaso Fernández-Irisarri and Manuel Mañas. Laguerre-Freud Equations for three families of hypergeometric discrete orthogonal polynomials. Studies in Applied Mathematics 151 (2023), 509-535. doi:10.1111/sapm.12601 .JIF percentile: 91.7.
  16. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Bidiagonal factorization of tetradiagonal matrices and Darboux transformations. Analysis and Mathematical Physics 13 (2023), article number 42. doi:10.1007/s13324-023-00801-1. JIF percentile: 88.4.


    2022

  17. Gerardo Ariznabarreta and Manuel Mañas. Multivariate orthogonal Laurent polynomials and integrable systems. Publications of the Research Institute for Mathematical Sciences, Kyoto University 58.1 (2022), 79–185. doi:10.4171/PRIMS/58-1-4. JIF percentile: 72.6.
  18. Gerardo Ariznabarreta and Manuel Mañas. Multivariate Toda hierarchies and biorthogonal polynomials. Physica D: Nonlinear Phenomena 434 (2022), 133202. doi:10.1016/j.physd.2022.133202. JIF percentile: 94.19.
  19. Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi, and Manuel Mañas. Riemann–Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: the Matrix Discrete Painlevé IV. Mathematics 10 (2022), 1205. doi:10.3390/math10081205. JIF percentile: 93.2.
  20. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Multiple orthogonal polynomials: Pearson equations and Christoffel formulas. Analysis and Mathematical Physics 12 (2022), paper 129. doi:10.1007/s13324-022-00734-1. JIF percentile: 84.7.
  21. Manuel Mañas. Pearson Equations for Discrete Orthogonal Polynomials: III. Christoffel and Geronimus transformations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 116 (2022), article number 128 . doi:10.1007/s13398-022-01296-4. JIF percentile: 95.6.
  22. Manuel Mañas, Itsaso Fernández-Irisarri, and Omar González-Fernández. Pearson Equations for Discrete Orthogonal Polynomials: I. Generalized Hypergeometric Functions and Toda Equations. Studies in Applied Mathematics 148 (2022), 1141–1179. doi:10.1111/sapm.12471. JIF percentile: 86.3.


    2021

  23. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Matrix Biorthogonal Polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. Journal of Mathematical Analysis and Applications 494.2 (2021), 124605. doi:10.1016/j.jmaa.2020.124605. JIF percentile: 77.03.


    2019

  24. Gerardo Ariznabarreta, Juan Carlos García-Ardila, Manuel Mañas, and Francisco Marcellán. Matrix biorthogonal polynomials on the real line: Geronimus transformations. Bulletin of Mathematical Sciences 9.2 (2019), 1950007 (68 pages). doi:10.1007/s13373-018-0128-y, doi:10.1142/S1664360719500073. JIF percentile: 92.197.
  25. Giovanni Cassatella-Contra and Manuel Mañas. Riemann-Hilbert problem and matrix discrete Painlevé II systems. Studies in Applied Mathematics 143.3 (2019), 273–314. doi:10.1111/sapm.12277. JIF percentile: 95.211.
  26. Juan Carlos García-Ardila, Manuel Mañas, and Francisco Marcellán. Christoffel transformation for a matrix of bi-variate measures. Complex Analysis and Operator Theory 13 (2019), 3979–4005. doi:10.1007/s11785-019-00947-6. JIF percentile: 46.019.


    2018

  27. Gerardo Ariznabarreta, Juan Carlos García-Ardila, Manuel Mañas, and Francisco Marcellán. Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations. Journal of Physics A: Mathematical & Theoretical 51 (2018), 205204. doi:10.1088/1751-8121/aab9ca. JIF percentile: 82.727.
  28. Gerardo Ariznabarreta and Manuel Mañas. Christoffel transformations for multivariate orthogonal polynomials. Journal of Approximation Theory 225 (2018), 242–283. doi:10.1016/j.jat.2017.10.007. JIF percentile: 72.134.
  29. Gerardo Ariznabarreta, Manuel Mañas, and Alfredo Toledano. CMV biorthogonal Laurent polynomials: perturbations and Christoffel formulas. Studies in Applied Mathematics 140.3 (2018), 333–400. doi:10.1111/sapm.12202. JIF percentile: 91.142.


    2017

  30. Carlos Álvarez-Fernández, Gerardo Ariznabarreta, Juan Carlos García-Ardila, Manuel Mañas, and Francisco Marcellán. Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy”. International Mathematics Research Notices 2017.5 (2017), 1285–1341. doi:10.1093/imrn/rnw027. JIF percentile: 89.516.

    2016

  31. Gerardo Ariznabarreta and Manuel Mañas. Multivariate orthogonal polynomials and integrable systems. Advances in Mathematics 302 (2016), 628–739. doi:10.1016/j.aim.2016.06.029. JIF percentile: 91.479.


    2015

  32. Gerardo Araznibarreta and Manuel Mañas. A Jacobi type Christoffel-Darboux formula for multiple orthogonal polynomials of mixed type. Linear Algebra and its Applications 468 (2015), 154–170. doi:10.1016/j.laa.2014.04.030. JIF percentile: 87.340.

    2014

  33. Carlos Álvarez-Fernández and Manuel Mañas. On the Christoffel–Darboux formula for generalized matrix orthogonal polynomials. Journal of Mathematical Analysis and Applications 418.1 (2014), 238–247. doi:10.1016/j.jmaa.2014.03.094. JIF percentile: 79.647.
  34. Gerardo Ariznabarreta and Manuel Mañas. Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems. Advances in Mathematics 264 (2014), 396–463. doi:10.1016/j.aim.2014.06.019. JIF percentile: 90.865.
  35. Giovanni A Cassatella-Contra, Manuel Mañas, and Piergiulio Tempesta. Singularity confinement for matrix discrete Painlevé Equations. Nonlinearity 27 (2014), 2321. doi:10.1088/0951-7715/27/9/2321. JIF percentile: 74.514.

    2013

  36. Carlos Álvarez-Fernández and Manuel Mañas. Orthogonal Laurent polynomials on the unit circle, extended CMV ordering and 2D Toda type integrable hierarchies. Advances in Mathematics 240 (2013), 132–193. doi:10.1016/j.aim.2013.02.020. JIF percentile: 93.543.

    2012

  37. Giovanni Angello Cassatella-Contra and Manuel Mañas. Riemann–Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement. Studies in Applied Mathematics 128.3 (2012), 252–274. doi:10.1111/j.1467-9590.2011.00541.x. JIF percentile: 81.174.

    2011

  38. Carlos Álvarez-Fernández, Ulises Fidalgo Prieto, and Manuel Mañas. Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy. Advances in Mathematics 227 (2011), 1451–1525. doi:10.1016/j.aim.2011.03.008. JIF percentile: 90.830.

    2010

  39. Carlos Álvarez-Fernández, Ulises Fidalgo Prieto, and Manuel Mañas. The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems. Inverse Problems 26 (2010), 055009. doi:10.1088/0266-5611/26/5/055009. JIF percentile: 95.551.
  40. Guido Carlet and Manuel Mañas. On the Lax representation of the 2-component KP and 2D Toda hierarchies. Journal of Physics A: Mathematical & Theoretical 43 (2010), 434011. doi:10.1088/1751-8113/43/43/434011. JIF percentile: 69.44.
  41. David Gómez-Ullate, Sara Lombardo, Manuel Mañas, Marta Mazzocco, Frank Nijhoff, and Matteo Sommacal. Integrability and nonlinear phenomena. Journal of Physics A: Mathematical & Theoretical 43 (2010), 430301. doi:10.1088/1751-8121/43/43/430301. JIF percentile: 69.44.
  42. Runliang Lin, Hua Peng, and Manuel Mañas. The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons. Journal of Physics A: Mathematical and Theoretical 43 (2010), 434022. doi:10.1088/1751-8113/43/43/434022. JIF percentile: 69.44.

    2009

  43. Manuel Mañas and Luis Martínez Alonso. The multicomponent 2D Toda hierarchy: dispersionless limit. Inverse Problems 25 (2009), 115020. doi:10.1088/0266-5611/25/11/115020. JIF percentile: 93.38.
  44. Manuel Mañas, Luis Martínez Alonso, and Carlos Álvarez-Fernández. The multicomponent 2D Toda hierarchy: discrete flows and string equations. Inverse Problems 25 (2009), 065007. doi:10.1088/0266-5611/25/6/065007. JIF percentile: 93.38.

    2006

  45. Manuel Mañas, Elena Medina, and Luis Martínez Alonso. On the Whitham hierarchy: dressing scheme, string equations and additional symmetries. Journal of Physics A: Mathematical & General 39 (2006), 2349–2381. doi:10.1088/0305-4470/39/10/008. JIF percentile: 69.51.
  46. Luis Martínez Alonso, Elena Medina, and Manuel Mañas. String equations in Whitham hierarchies: τ-functions and Virasoro constraints. Journal of Mathematical Physics 47 (2006), 83512–83522. doi:10.1063/1.2218982. JIF percentile: 47.56.

    2004

  47. Manuel Mañas. S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies. Journal of Physics A: Mathematical & General 37 (2004), 11191–11221. doi:10.1088/0305-4470/37/46/007. JIF percentile: 69.12.
  48. Manuel Mañas. On the r-th dispersionless Toda hierarchy: factorization problem, additional symmetries and some solutions. Journal of Physics A: Mathematical & General 37 (2004), 9195–9224. doi:10.1088/0305-4470/37/39/010. JIF percentile: 69.12.
  49. Manuel Mañas and Luis Martínez Alonso. A hodograph transformation which applies to the Boyer–Finley equation. Physics Letters A 320.5-6 (2004), 383–388. doi:10.1016/j.physleta.2003.10.023. JIF percentile: 64.93.

    2003

  50. Francisco Guil, Manuel Mañas, and Luis Martínez Alonso. On twistor solutions of the dKP equation. Journal of Physics A: Mathematical & General 36 (2003), 6457–6472. doi:10.1088/0305-4470/36/23/311. JIF percentile: 69.35.
  51. Francisco Guil, Manuel Mañas, and Luis Martínez Alonso. The Whitham hierarchies: reductions and hodograph solutions. Journal of Physics A: Mathematical & General 36 (2003), 4047–4062. doi:10.1088/0305-4470/36/14/309. JIF percentile: 69.35.
  52. Manuel Mañas and Luis Martínez Alonso. A hodograph transformation applicable to a large class of PDEs. Theoretical and Mathematical Physics 137.2 (2003), 1544–1549. doi:10.1023/A:1027313919457. JIF percentile: 33.87.
  53. Luis Martínez Alonso and Manuel Mañas. Additional symmetries and solutions of the dispersionless KP hierarchy in Integrability, topological solitons and beyond. Journal of Mathematical Physics 44.8 (2003), 3294–3308. doi:10.1063/1.1587873. JIF percentile: 72.58.

    2002

  54. Manuel Mañas. From integrable nets to integrable lattices. Journal of Mathematical Physics 43.5 (2002), 2523–2546. doi:10.1063/1.1454185. JIF percentile: 70.69.
  55. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Explicit solutions of integrable lattices. Journal of Geometry and Physics 42.3 (2002), 195–215. doi:10.1016/S0393-0440(01)00085-7. JIF percentile: 60.34.
  56. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Reductions and hodograph solutions of the dispersionless KP hierarchy. Journal of Physics A: Mathematical & General 35 (2002), 401–417. doi:10.1088/0305-4470/35/2/316. JIF percentile: 77.59.
  57. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Reductions of the dispersionless KP hierarchy. Theoretical and Mathematical Physics 133.3 (2002), 1712–1721. doi:10.1023/A:1021322527060. JIF percentile: 18.97.

    2001

  58. Manuel Mañas. Fundamental transformations for quadrilateral lattices: first potentials and τ-functions, symmetric and pseudo-Egorov reductions. Journal of Physics A: Mathematical & General 34 (2001), 10413–10421. doi:10.1088/0305-4470/34/48/307. JIF percentile: 77.59.
  59. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. KP theory of Egorov nets. Theoretical and Mathematical Physics 127.3 (2001), 800–807. doi:10.1023/A:1010455903098. JIF percentile: 22.41.

    2000

  60. Adam Doliwa, Paolo Maria Santini, and Manuel Mañas. Transformations of quadrilateral lattices. Journal of Mathematical Physics 41 (2000), 944–990. doi:10.1063/1.533175. JIF percentile: 50.00.
  61. Qing Ping Liu and Manuel Mañas. Darboux transformations for super-symmetric KP hierarchies. Physics Letters B 485.1-3 (2000), 293–300. doi:10.1016/S0370-2693(00)00663-8. JIF percentile: 90.00.
  62. Manuel Mañas. Nets, lattices, and multicomponent KP hierarchies. Theoretical and Mathematical Physics 122.2 (2000), 229–238. doi:10.1007/BF02551199. JIF percentile: 22.41.
  63. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Dressing methods for geometric nets: I. Conjugate nets. Journal of Physics A: Mathematical & General 33 (2000), 2871–2894. doi:10.1088/0305-4470/33/14/317. JIF percentile: 77.59.
  64. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Dressing methods for geometric nets: II. Orthogonal and Egorov nets. Journal of Physics A: Mathematical & General 33 (2000), 7181–7206. doi:10.1088/0305-4470/33/40/314. JIF percentile: 77.59.

    1999

  65. Adam Doliwa, Manuel Mañas, and Luis Martínez Alonso. Generating quadrilateral and circular lattices in KP theory. Physics Letters A 262.4-5 (1999), 330–343. doi:10.1016/S0375-9601(99)00579-4. JIF percentile: 63.85.
  66. Adam Doliwa, Manuel Mañas, Luis Martínez Alonso, Elena Medina, and Paolo Maria Santini. Charged free fermions, vertex operators and the classical theory of conjugate nets. Journal of Physics A: Mathematical & General 32 (1999), 1197–1216. doi:10.1088/0305-4470/32/7/010. JIF percentile: 82.00.
  67. Qing Ping Liu and Manuel Mañas. Symmetric reduction of the vectorial fundamental transformation: application to the Darboux–Egorov equations. Journal of Physics A: Mathematical & General 32 (1999), 5921. doi:10.1088/0305-4470/32/32/307. JIF percentile: 82.00.
  68. Qing Ping Liu and Manuel Mañas. Vectorial Darboux transformations for the Kadomtsev–Petviashvili hierarchy. Journal of Nonlinear Science 9.2 (1999), 213–232. doi:10.1007/s003329900070. JIF percentile: 94.57.
  69. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Hidden hierarchies of KdV type on Birkhoff strata. Journal of Geometry and Physics 29.1 (1999), 13–34. doi:10.1016/S0393-0440(98)00029-1. JIF percentile: 46.00.

    1998

  70. Qing Ping Liu and Manuel Mañas. Discrete Levy transformations and Casorati determinant solutions of quadrilateral lattices. Physics Letters A 239.3 (1998), 159–166. doi:10.1016/S0375-9601(97)00933-X. JIF percentile: 66.92.
  71. Qing Ping Liu and Manuel Mañas. Pfaffian solutions for the Manin-Radul-Mathieu SUSY KdV and SUSY sine-Gordon equations. Physics Letters B 436.3-4 (1998), 306–310. doi:10.1016/S0370-2693(98)00852-1. JIF percentile: 90.00.
  72. Qing Ping Liu and Manuel Mañas. Sequences of Lévy transformations and multi-Wroński determinant solutions of the Darboux equations. Journal of Geometry and Physics 27 (1998), 178–184. doi:10.1016/S0393-0440(97)00074-0. JIF percentile: 23.91.
  73. Qing Ping Liu and Manuel Mañas. Superposition formulæ for the discrete Ribacour transformations of circular lattices. Physics Letters A 249.5 (1998), 424–430. doi:10.1016/S0375-9601(98)00721-X. JIF percentile: 66.92.
  74. Qing Ping Liu and Manuel Mañas. Vectorial Ribacour transformations for the Lamé equations. Journal of Physics A: Mathematical & General 31 (1998), L193–L200. doi:10.1088/0305-4470/31/10/003. JIF percentile: 82.00.
  75. Manuel Mañas and Luis Martínez Alonso. From Ramond fermions to Lamé equations for orthogonal curvilinear coordinates. Physics Letters B 436.3-4 (1998), 316–322. doi:10.1016/S0370-2693(98)00851-X. JIF percentile: 90.00.

    1997

  76. Francisco Guil and Manuel Mañas. The Darboux system: Finite-rank constraints and Darboux transformations. Journal of Mathematical Physics 38 (1997), 5968–5975. doi:10.1063/1.532174. JIF percentile: 54.00.
  77. Qing Ping Liu and Manuel Mañas. Crum transformation and Wronskian type solutions for supersymmetric KdV equation. Physics Letters B 396 (1997), 133–140. doi:10.1016/S0370-2693(97)00134-2. JIF percentile: 91.27.
  78. Qing Ping Liu and Manuel Mañas. Darboux transformation for the Manin-Radul supersymmetric KdV equation. Physics Letters B 394.3-4 (1997), 337–342. doi:10.1016/S0370-2693(97)00026-9. JIF percentile: 91.27.
  79. Manuel Mañas, Adam Doliwa, and Paolo Maria Santini. Darboux transformations for multidimensional quadrilateral lattices. I. Physics Letters A 232.1 (1997), 99–105. doi:10.1016/S0375-9601(97)00341-1. JIF percentile: 70.63
  80. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Zero sets of -functions and hidden hierarchies of KdV type. Journal of Physics A: Mathematical & General 30 (1997), 4815–4824. doi:10.1088/0305-4470/30/13/029. JIF percentile: 78.00.
  81. Manuel Mañas and Paolo Maria Santini. Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction. Physics Letters A 227.5-6 (1997), 325–334. doi:10.1016/S0375-9601(97)00045-5. JIF percentile: 70.63.

    1996

  82. Francisco Guil and Manuel Mañas. Darboux transformations for the Davey–Stewartson equations. Physics Letters A 217.1 (1996), 1–6. doi:10.1016/0375-9601(96)00304-0. JIF percentile: 70.63.
  83. Francisco Guil and Manuel Mañas. The Dirac equation and integrable systems of KP type. Journal of Physics A: Mathematical & General 29  (1996), 641–665. doi:10.1088/0305-4470/29/3/016. JIF percentile: 78.00.
  84. Manuel Mañas. Darboux transformations for the nonlinear Schrödinger equations. Journal of Physics A: Mathematical & General 29  (1996), 7721–7737. doi:10.1088/0305-4470/29/23/029. JIF percentile: 78.00.

    1995

  85. Francisco Guil and Manuel Mañas. Deformation of the dromion and solitoff solutions of the Davey–Stewartson I equation. Physics Letters A 209.1 (1995), 39–47. doi:10.1016/0375-9601(95)00783-3. JIF percentile: 70.63.
  86. Francisco Guil and Manuel Mañas. Finite-rank constraints on linear flows and the Davey–Stewartson equation. Journal of Physics A: Mathematical & General 28 (1995), 1713–1726. doi:10.1088/0305-4470/28/6/023. JIF percentile: 78.00.
  87. Francisco Guil and Manuel Mañas. The Davey–Stewartson equation and constrained linear flows. Physica D: Nonlinear Phenomena 87  (1995), 99–104. doi:10.1016/0167-2789(95)00153-U. JIF percentile:76.98.
  88. Manuel Mañas. The geometry of the Hermitian matrix model and lattices for the NLS and dNLS hierarchies. Journal of Geometry and Physics 17.1 (1995), 1–24. doi:10.1016/0393-0440(94)00037-5. JIF percentile: 30.00.
  89. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Additional symmetries for super KP hierarchies. Physica D: Nonlinear Phenomena 87 (1995), 105–108. doi:10.1016/0167-2789(95)00154-V. JIF percentile: 76.98.

    1994

  90. Francisco Guil and Manuel Mañas. AKNS hierarchy, self-similarity, string equations and the Grassmannian. Journal of Physics A: Mathematical & General 27 (1994), 2129–2142. doi:10.1088/0305-4470/27/6/034. JIF percentile: 78.00.
  91. Francisco Guil and Manuel Mañas. Two-dimensional integrable systems and self-dual Yang–Mills equations. Journal of Mathematical Physics 35.6 (1994), 2902–2913. doi:10.1063/1.530493. JIF percentile: 54.00.
  92. Francisco Guil, Manuel Mañas, and Gabriel Álvarez Galindo. The Hopf–Cole transformation and the KP equation. Physics Letters A 190.1 (1994), 49–52. doi:10.1016/0375-9601(94)90364-6. JIF percentile: 70.63.
  93. Manuel Mañas. The Hermitian matrix model and homogeneous spaces. Theoretical and Mathematical Physics 99.2 (1994), 635–640. doi:10.1007/BF01016151. JIF percentile: 10.00.
  94. Manuel Mañas and Partha Guha. String equations for the unitary matrix model and the periodic flag manifold. Communications in Mathematical Physics 161.2 (1994), 215–232. doi:10.1007/BF02099775. JIF percentile: 86.00.
  95. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Additional symmetries, Virasoro constraints and string equations for super KP hierarchies. Physics Letters B 336 (1994), 178–182. doi:10.1016/0370-2693(94)00904-X. JIF percentile: 91.27.

    1993

  96. Francisco Guil and Manuel Mañas. Nahm equations and self-dual Yang–Mills equations. Physics Letters B 302.4 (1993), 431–434. doi 10.1016/0370-2693(93)90422-E. JIF percentile: 91.27.
  97. Francisco Guil and Manuel Mañas. String equations for the KdV hierarchy and the Grassmannian. Journal of Physics A: Mathematical & General 26 (1993), 3569–3582. doi:10.1088/0305-4470/26/14/021. JIF percentile: 78.00.
  98. Manuel Mañas. Scaling self-similar formulation of the string equations of the Hermitian one-matrix model. Physics Letters B 317.1 (1993), 341–345. doi:10.1016/0370-2693(93)91005-8. JIF percentile: 91.27.
  99. Manuel Mañas, Juan Manuel R Parrondo, and Francisco Javier de la Rubia. System-reservoir interaction with stochastic coupling parameters. Journal of Statistical Physics 71.5 (1993), 1157–1169. doi:10.1007/BF01049964. JIF percentile: 90.00.

    1991

  100. Francisco Guil and Manuel Mañas. Homogeneous manifolds and modified KdV equations. Journal of Mathematical Physics 32 (1991), 1744–1749. doi:10.1063/1.529236. JIF percentile: 54.00.
  101. Francisco Guil and Manuel Mañas. Loop algebras and the Krichever–Novikov equation. Physics Letters A 153.2-3 (1991), 90–94. doi:10.1016/0375-9601(91)90845-Y. JIF percentile: 70.63.

    1990

  102. Francisco Guil and Manuel Mañas. The homogeneous Heisenberg subalgebra and equations of AKNS type. Letters in Mathematical Physics 19.2 (1990), 89–95. doi:10.1007/BF01045878. JIF percentile: 38.00.
  103. Juan Manuel R Parrondo, Manuel Mañas, and F. Javier Rubia. Geometrical treatment of systems driven by coloured noise. Journal of Physics A: Mathematical & General 23 (1990), 236–2378. doi:10.1088/0305-4470/23/12/018. JIF percentile: 78.00.

Non JCR papers

Qing Ping Liu and Manuel Mañas. On the Pfaffian solutions of the BKP hierarchy. Chinese Annals of Mathematics Series A 23.6 (2002), 693–698 (in chinese)

Under review

  1. Amilcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, Hélder Lima and Manuel Mañas, Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality, 2024. arXiv:2410.15363
  2. Amilcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, Manuel Mañas, and Thomas Wolfs, Classical discrete multiple orthogonal polynomials: hypergeometric and integral representations, 2024, arXiv:2409.16254 
  3. Amilcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, Manuel Mañas, and Thomas Wolfs, Integral and hypergeometric representations for multiple orthogonal polynomials, 2024. arXiv: 2407.15001 
  4. Itsaso Fernández-Irisarri, Manuel Mañas, Toda and Laguerre-Freud equations for multiple discrete orthogonal polynomials with an arbitrary number of weights, 2024. arXiv: 2407.00777 
  5. Manuel Mañas and Miguel Rojas. General Christoffel perturbations for mixed multiple orthogonal polynomials, 2024. arXiv:2405.11630 
  6. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Banded totally positive matrices and normality for mixed multiple orthogonal polynomials, 2024. arxiv:2404.13965 
  7. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation, 2024. arxiv:2404.13958 
  8. Amilcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Hypergeometric Multiple Orthogonal Polynomials and Random Walks. 2021. arXiv: 2107.00770 

Books

  1. Manuel Mañas and  Luis Martínez Alonso, Boundary Value Problems for Linear Partial Differential Equations.Chapman and Hall/CRC (Taylor & Francis group), 2024. ISBN:978-1-0326-6252-7. doi:10.1201/9781032664514.
  2. Alexei Borisevich Shabat, Artemio González-López,Manuel Mañas, Luis Martínez Alonso, and Miguel Ángel Rodríguez, eds. New trends in integrability and partial solvability. Vol. 132. NATO Science Series: II. Mathematics, Physics and Chemistry. Dordrecht: Kluwer, 2004. ISBN:978-1-4020-1835-0.  doi:10.1007/978-94-007-1023-8.
  3. Artemio González-López, Manuel Mañas, Luis Martínez Alonso, and Miguel Ángel Rodríguez, eds. X Fall Workshop on Geometry and Physics. Vol. 4. Publicaciones de la Real Sociedad Española de Matemáticas. Miraflores de la Sierra, Madrid, Spain, 2003. ISBN 84-923818-8-4.

Book chapters

  1. Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi, and Manuel Mañas, Matrix Orthogonal Polynomials: A Riemann-Hilbert approach in Orthogonal Polynomials and Special Functions. In Memory of José Carlos Petronilho, Kenier Castillo and Antonio J. Durán, editors. Coimbra Mathematical Texts 3, Springer, 2025.ISBN:978-3-031-69645-9.
  2. Amílcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Banded matrices and their orthogonality in  Recent Progress in Special Functions, Galina Filipuk, editor. AMS Contemporary Mathematics 807 (2024) 1-17. doi: 10.1090/conm/807/16163.
  3. Manuel Mañas and Luis Martínez Alonso. Integrable nets and the KP hierarchy. In Integrable Hierarchies and Modern Physical Theories. Vol. 18. NATO Science Series. II: Mathematics, Physics and Chemistry. Chicago, IL, USA: Kluwer, 2001, 391–422. doi:10.1007/978-94-010-0720-7_15.
  4. Manuel Mañas. The Principal Chiral Model as an Integrable System.  In Harmonic maps and integrable systems. Vol. 23. Aspects in Mathematics E. Vieweg Verlag (re-edited by Springer (2014)), 1994, 147–174. doi:10.1007/978-3-663-14092-4_7.

Proceedings

  1. Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno, and Manuel Mañas. Markov Chains and Multiple Orthogonality, To appear in Orthogonal Polynomials, Special Functions and Applications - Proceedings of the 16th International Symposium, Montreal, Canada, In honor to Richard Askey in the CRM Series in Mathematical Physics, Springer, 2024.
  2. Amilcar Branquinho, Ana Foulquié-Moreno, and Manuel Mañas. Riemann–Hilbert problem and Matrix Biorthogonal Polynomials. EIBPOA: Iberoamerican school on orthogonal polynomials and applications 2018. SEMA SIMAI Springer Series. Springer Verlag, 2021. doi:10.1007/978-3-030-56190-1_1.
  3. Manuel Mañas. Revisiting biorthogonal polynomials. An LU factorization discussion. EIBPOA: Iberoamerican school on orthogonal polynomials and applications 2018. SEMA SIMAI Springer Series. Springer Verlag, 2021. doi:10.1007/978-3-030-56190-1_10.
  4. Manuel Mañas. Whitham hierarchies: dressing, string equations and additional symmetries. Riemann–Hilbert Problems, Integrability and Asymptotics. Ed. by Simonetta Abenda, Boris Dubrovin, Gregorio Falqui, and Tamara Grava. Trieste, Italy, 2005. url: http://misgam.sissa.it/RHPIA05/talks/.
  5. Jesús Calvo and Manuel Mañas. Novel Solutions of Davey Stewartson II Equation.  X Fall Workshop on Geometry and Physics. Ed. by Artemio González-López, Manuel Mañas, Luis Martínez Alonso, and Miguel Ángel Rodríguez. Vol. 4. Publicaciones de la Real Sociedad Española de Matemáticas. Miraflores de la Sierra, Madrid, Spain, 2003, 77–84. ISBN 84-923818-8-4.
  6. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Dressing Methods for Geometric Nets. Octavo Encuentro de Otoño de Geometría y Física. Ed. by Mariano del Olmo and Mariano Santander. Vol. 2. Publicaciones de la Real Sociedad Española de Matemáticas. Medina del Campo, Valladolid, Spain, 2001, 181–194. ISBN 84-923818-4-1.
  7. Qing Ping Liu and Manuel Mañas. Darboux transformations for SUSY integrable systems. Supersymmetry and Integrable Models. Ed. by H. Aratyn, T. Imbo, W.-Y. Keung, and U. Sukhatme. Vol. 502. Lecture Notes Physics. Supersymmetry and integrable systems. Chicago, IL, USA: Springer, 1998, 268–281. doi:10.1007/BFb0105324.
  8. Manuel Mañas, Luis Martínez Alonso, and Elena Medina. Loop groups, Birkhoff Strata and Hidden KdV Hierarchies. Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras. GROUP21. Ed. by H.-D. Doebner, W. Scherer, and C. Schulte. Goslar, Germany: World Scientific, 1997, 1057–1059. doi:10.1142/3473.
  9. Francisco Guil and Manuel Mañas. Multi-Dimensional Davey-Stewartson Systems and Linear Flows. Explicit Solutions. Nonlinear Evolution Equations & Dynamical Systems Needs ’94. (10th International Workshop). Ed. by V. G. Makhankov, A. R. Bishop, and D. Holm. Los Alamos, NM, USA: World Scientific, 1995, 150–157. doi:10.1142/9789814532945.
  10. Manuel Mañas. The 2D Dirac equation and the Davey–Stewartson II Equation: Deformation of the dromion solutions. Coherent Structures in Physics and Biology. Ed. by J. C. Eilbeck. Edinburgh, UK, 1995. url: http://www.ma.hw.ac.uk/solitons/procs/. Broken link.
  11. Manuel Mañas. Virasoro Constraints and String Equations for the Jacobian Super KP Hierarchy. Nonlinear Evolution Equations & Dynamical Systems Needs ’94. (10th International Workshop). Ed. by V. G. Makhankov, A. R. Bishop, and D. Holm. Los Alamos, NM, USA: World Scientific, 1995, 150–157. doi:10.1142/9789814532945.
  12. Francisco Guil and Manuel Mañas. Self-Dual Yang-Mills Equations and the Principal Chiral Model. Nonlinear Evolution Equations and Dynamical Systems. Proceedings of the 8th International Workshop (NEEDS’92). Ed. by V. G. Makhankov, I. V. Puzynin, and O. K. Pashaev. Dubna, Rusia: World Scientific, 1993, 211–213. doi:10.1142/9789814535601.
  13. Manuel Mañas. Self-Similarity in the KdV Hierarchy. Geometry of the String Equations. Nonlinear Evolution Equations and Dynamical Systems. Proceedings of the 8th International Workshop (NEEDS’92). Ed. by V. G. Makhankov, I. V. Puzynin, and O. K. Pashaev. Dubna, Rusia: World Scientific, 1993, 261–270. doi:10.1142/9789814535601.
  14. Francisco Guil and Manuel Mañas. Integrable systems of the KdV and NLS type and self—dual Yang-Mills equations. Group Theoretical Methods in Physics. GROUP19. Ed. by Mariano del Olmo, Mariano Santander, and Juan Mateos. Vol. 1. Anales de Física, Monografías. Salamanca, Spain, 1992, 253–255. ISBN 84-7834-159-5.
  15. Manuel Mañas. “Homogeneous Manifolds, Factorisation Problems and Modified KdV Equations”. Nonlinear Evolution Equations and Dynamical Systems’90. Ed. by V. G. Makhankov and O. K. Pashaev. Reports in Physics. Dubna, Union of Soviet Socialist Republics: Springer, 1991, 110–116. doi:10.1007/978-3-642-76172-0_23.

PhD thesis

Manuel Mañas Baena, Problemas de factorización y sistemas integrables. 1991

Supervised PhD thesis

  1. Carlos Álvarez Fernández, Orthogonal polynomials and integrable systems. 2014
  2. Giovanni Cassatella Contra, Discrete integrable systems, matrix orthogonal polynomials and Riemann-Hilbert problems. 2016 
  3. Gerardo Ariznabarreta García de Cortázar, Biorthogonal polynomials and their generalizations: a perspective from integrable systems. 2018

PhD thesis on progress

  1. Juan Enrique Fernández Díaz, Multiple orthogonal polynomials and applications
  2. Itsaso Fernández Irisarri, Hypergeometric discrete orthogonal polynomials