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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[...]![]()
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Single-field inflaton models in the kinetic dominance period admit formal solutions given by generalized asymptotic expansions called psi series. We present a method for computing psi series for the Hubble parameter as a function of the inflaton[...]![]()
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Álvarez Galindo, Gabriel ; Martínez Alonso, Luis ; Medina Reus, Elena | IOP publishing ltd | 2011-07-15We present a method to characterize and compute the large N formal asymptotics of regular and critical Hermitian matrix models with general even potentials in the one-cut and two-cut cases. Our analysis is based on a method to solve continuum li[...]![]()
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The DaveyStewartson equation is considered from the point of view of the bilinear formalism of the Kyoto school. Multidromion solutions are constructed in terms of free fermions and their asymptotic properties are characterized. The dynamical pr[...]![]()
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The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the pha[...]![]()
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Jaulent, Marcel ; Manna, Miguel A. ; Martínez Alonso, Luis | American Institute of Physics | 1989-08A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized[...]![]()
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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[...]![]()
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The relationship between the soliton dynamics provided by the classical sine-Gordon and massive Thirring models is exhibited. Solitons are characterized as classical relativistic particles through the consideration of their associated canonical [...]![]()
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A method is given for finding the shifts in position of the solitons for the case of nonzero reflection coefficient. Expressions for boost generators in terms of scattering data play a prominent role in the analysis. Phase-shift formulas which s[...]![]()
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The effect of the radiation modes on soliton motion in nonlinear lattices is investigated. A method based on the inverse scattering transform is developed, which enables us to characterize the position shifts of solitons due to their interaction[...]![]()
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Solutions of the Riemann-Hilbert problem implementing the twistorial structure of the dispersionless Toda (dToda) hierarchy are obtained. Two types of string equations are considered which characterize solutions arising in hodograph sectors and [...]![]()
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We study the moduli space of the spectral curves y ^2 = W ‘ (z) ^2 + f(z) which characterize the vacua of N = 1 U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential W(z). The integrable structure o[...]