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Autor Martínez Alonso, Luis |
Documentos disponibles escritos por este autor (62)
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A class of nonlinear problems on the plane, described by nonlinear inhomogeneous ?¯-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources), is described by Hamilton–Jacob[...]![]()
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The one-cut case of the Hermitian random matrix model in the large N limit is considered. Its singular sector in the space of coupling constants is analyzed from the point of view of the hodograph equations of the underlying dispersionless Toda [...]![]()
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A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations[...]![]()
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Guil Guerrero, Francisco ; Mañas Baena, Manuel ; Martínez Alonso, Luis | IOP Publishing | 2003-06-13The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for[...]![]()
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We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to determine [...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | IOP publishing ltd | 2017-03-24The partition function of the Penner matrix model for both positive and negative values of the coupling constant can be explicitly written in terms of the Barnes G function. In this paper we show that for negative values of the coupling constant[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Elsevier Science BV | 2015-08-15We apply the method we have described in a previous paper (2013) to determine the phase structure of asymptotic zero densities of the standard cubic model of non-Hermitian orthogonal polynomials. We provide a complete description of the two phas[...]![]()
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We present a method for studying phase transitions in the large N limit of matrix models using matched solutions of Whitham hierarchies. The endpoints of the eigenvalue spectrum as functions of the temperature are characterized both as solutions[...]![]()
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We give a positive answer to a question about the existence of any direct link between two apparently unrelated facts for a specific family of solvable Lie algebras: the structure of their modules of functions on one side, and the algebraic form[...]![]()
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A ?¯formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions o[...]![]()
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Critical processes of ideal integrable models of Hele-Shaw flows are considered. A regularization method based on multiscaling expansions of solutions of the KdV and Toda hierarchies characterized by string equations is proposed. Examples are ex[...]![]()
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An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena ; Vázquez, Juan Luis | American Institute of Physics | 2020-04-01We consider separatrix solutions of the differential equations for inflaton models with a single scalar field in a zero-curvature Friedmann-Lemaitre-Robertson-Walker universe. The existence and properties of separatrices are investigated in the [...]![]()
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Konopelchenko, Boris ; Martínez Alonso, Luis ; Medina Reus, Elena | American Institute of Physics | 2000-01Integrable hierarchies associated with the singular sector of the Kadomtsev– Petviashvili (KP) hierarchy, or equivalently, with ?? operators of nonzero index are studied. They arise as the restriction of the standard KP hierarchy to submanifolds[...]![]()
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We completely describe the singular sectors of the one-layer Benney system (classical long-wave equation) and dispersionless Toda system. The associated Euler-Poisson-Darboux equations E(1/2, 1/2) and E(-1/2,-1/2) are the main tool in the analys[...]