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Autor Mañas Baena, Manuel |
Documentos disponibles escritos por este autor (42)
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n this paper, matrix orthogonal polynomials in the real line are described in terms of a RiemannHilbert problem. This approach provides an easy derivation of discrete equations for the corresponding matrix recursion coefficients. The discrete eq[...]![]()
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We introduce an S-function formulation for the recently found rth dispersionless modified KP and rth dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a re[...]![]()
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The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarc[...]![]()
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Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formu[...]![]()
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Cassatella-Contra, Giovanni A ; Mañas Baena, Manuel ; Tempesta, Piergiulio | IOP publishing ltd | 2014-09We study the analytic properties of a matrix discrete system introduced by Cassatella and Manas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters [...]![]()
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The periodic flag manifold (in the Sato Grassmannian context) description of the modified Korteweg-de Vries hierarchy is used to analyse the translational and scaling self-similar solutions of this hierarchy. These solutions are characterized by[...]![]()
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Martínez Alonso, Luis ; Medina Reus, Elena ; Mañas Baena, Manuel | American Institute of Physics | 2006-08A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The ?-functions of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characte[...]![]()
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Martínez Alonso, Luis ; Medina Reus, Elena ; Mañas Baena, Manuel | American Institute of Physics | 2006-08A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are charact[...]![]()
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The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, whic[...]![]()
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The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated with an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov-Shabat equations are characterized. [...]![]()
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The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov-Schulman operators is introd[...]![]()
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We consider the relation of the multicomponent 2D Toda hierarchy with the matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polyn[...]![]()
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Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The q-mKPHSCSs contain two types of q-deformed mKP equation with self-co[...]![]()
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Guil Guerrero, Francisco ; Mañas Baena, Manuel ; Martínez Alonso, Luis | IOP Publishing | 2003-04-11A general scheme for analysing reductions of Whitham hierarchies is presented. It is based on a method for determining the S-function by means of a system of first-order partial differential equations. Compatibility systems of differential equat[...]![]()
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Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less tha[...]![]()
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We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type de[...]![]()
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The vectorial extension of the Ribaucour transformation for the Lame equations bf orthogonal conjugate nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data[...]