Person:
Martínez Alonso, Luis

First Name

Luis

Last Name

Martínez Alonso

URI

https://hdl.handle.net/20.500.14352/75166

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Físicas

Department

Física Teórica

Area

Física Teórica

Identifiers

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Now showing 1 - 10 of 30

String equations in Whitham hierarchies: τ-functions and Virasoro constraints
(Journal of mathematical physics, 2006) Martínez Alonso, Luis; Medina Reus, Elena; Mañas Baena, Manuel Enrique
A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The τ-functions of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated.
Quasiconformal mappings and solutions of the dispersionless KP hierarchy
(Theoretical and mathematical physics, 2002) Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, Elena
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 of the dKP hierarch.
Genus-zero Whitham hierarchies in conformal-map dynamics
(Physics letters B, 2006) Martínez Alonso, Luis; Medina Reus, Elena
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 show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are governed by genus-zero Whitham hierarchies.
Localized coherent structures of the Davey-Stewartson equation in the bilinear formalism
(Journal of mathematical physics, 1992) Martínez Alonso, Luis; Medina Reus, Elena
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 properties of dromions are discussed.
A classification of integrable quasiclassical deformations of algebraic curves
(Journal of physics A: Mathematical and general, 2006) Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, Elena
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 compatibility conditions for consistent deformations is given and expressions for the solutions of the corresponding Lenard relations are provided.
Regularization of Hele-Shaw flows, multiscaling expansions and the Painlevé I equation
(Chaos solitons & Fractals, 2009) Martínez Alonso, Luis; Medina Reus, Elena
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 exhibited in which the tritronquee solution of the Painleve-I equation turns out to provide the leading term of the regularization.
Exact solutions of integrable 2D contour dynamics
(Physics letters B, 2005) Martínez Alonso, Luis; Medina Reus, Elena
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-functions are determined and the emergence of cusps is studied.
An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
(Nuclear Physics B, 2011) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, Elena
We 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 deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.
Explicit solutions of supersymmetric KP hierarchies: Supersolitons and solitinos
(Journal of mathematical physics, 1996) Ibort, A.; Martínez Alonso, Luis; Medina Reus, Elena
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 KP theory, such as wave functions,δ̅ equations and τ-functions. Thus, supersymmetric generalizations of N-soliton solutions, including a new purely odd ‘‘solitino’’ solution, as well as rational solutions, are found and characterized.
Phase space and phase transitions in the Penner matrix model with negative coupling constant
(Journal of physics A: Mathematical and theoretical, 2017) Álvarez Galindo, Gabriel; Martínez Alonso, Luis; Medina Reus, Elena
The 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 this partition function can also be represented as the product of an holomorphic matrix integral by a nontrivial oscillatory function of n. We show that the planar limit of the free energy with 't Hooft sequences does not exist. Therefore we use a certain modification that uses Kuijlaars-McLaughlin sequences instead of 't Hooft sequences and leads to a well-defined planar free energy and to an associated two-dimensional phase space. We describe the different configurations of complex saddle points of the holomorphic matrix integral both to the left and to the right of the critical point, and interpret the phase transitions in terms of processes of gap closing, eigenvalue tunneling, and Bose condensation.