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Autor Martínez Alonso, Luis |
Documentos disponibles escritos por este autor (62)
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The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for dealing wit[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Elsevier Science BV | 2011-07-11We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its [...]![]()
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In this work we use Riemann-Hilbert problems for multiple orthogonal polynomials in order to derive string equations associated to Lax-Orlov pairs operators. These string equations provide us with a useful tool to analyze the large n-limit of th[...]![]()
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A previously introduced scheme for describing integrable deformations of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic-type systems. A general solution of the co[...]![]()
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It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in HeleShaw flows.![]()
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We give an exhaustive characterization of the complex saddle point configurations of the Gross-WittenWadia matrix model in the large-N limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, i[...]![]()
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The soliton dynamics in the complex sine-Gordon equation, massive Thirring model, and sine-Gordon equation are shown to be closely related.![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | 2013-06This paper deals with the determination of the S-curves in the theory of non-hermitian orthogonal polynomials with respect to exponential weights along suitable paths in the complex plane. It is known that the corresponding complex equilibrium p[...]![]()
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The quasiclassical limit of the scalar nonlocal ?? -problem is derived and a quasiclassical version of the ??-dressing method is presented. Dispersionless Kadomtsev– Petviashvili (KP), modified KP, and dispersionless two- dimensional Toda latt[...]![]()
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Mañas Baena, Manuel ; Martínez Alonso, Luis | Departamento de Física Teórica II (Métodos Matemáticos de la Física) | 2015En este manual se revisan diferentes aspectos sobre las ecuaciones diferenciales en derivadas parciales de utilidad para los físicos. Se elaboraron como notas de clase de la asignatura Ecuaciones II, del plan 1993 de la Licenciatura de Física de[...]![]()
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The problem of the soliton motion in the case of a nonzero reflection coefficient is solved exactly within the framework of the inverse scattering method. A general method is given for obtaining the asymptotic expressions of the soliton angle va[...]![]()
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A hierarchy of infinite-dimensional systems of hydrodynamic type is considered and a general scheme for classifying its reductions is provided. Wide families of integrable systems including, in particular, those associated with energy-dependent [...]![]()
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It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal hitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconfo[...]![]()
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A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding tau-funct[...]![]()
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Wide classes of explicit solutions of the Manin-Radul and Jacobian supersymmetric KP hierarchies are constructed by using line bundles over complex supercurves based on the Riemann sphere. Their construction extends several ideas of the standard[...]![]()
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Álvarez, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | Academic Press Inc Elsevier Science | 2015-10In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large n limit in the non-hermitian Penner matrix model. In these generalizations g_(n)n ? t, but the produ[...]![]()
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We show how Ramond free neutral Fermi fields lead to a ?-function theory of BKP type which describes iso-orthogonal deformations of systems of orthogonal curvilinear coordinates. We also provide a vertex operator representation for the classical[...]![]()
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The bilinear equations of the N-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical obj[...]![]()
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A scheme for solving quasiclassical-string equations is developed to prove that genus-zero hitham hierarchies describe the deformations of planar domains determined by rational conformal-maps. This property is applied in normal matrix models to[...]![]()
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We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We p[...]![]()
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We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We p[...]![]()
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We investigate the diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains and analyze their compatibility with previously introduced reductions of differential type.![]()
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We present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.![]()
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A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian[...]![]()
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Kodama, Y. ; Konopelchenko, Boris ; Martínez Alonso, Luis ; Medina Reus, Elena | American Institute of Physics | 2005-11A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize t[...]