Person: Martínez Alonso, Luis
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First Name
Luis
Last Name
Martínez Alonso
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Físicas
Department
Física Teórica
Area
Física Teórica
Identifiers
62 results
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Now showing 1 - 10 of 62
Item String equations in Whitham hierarchies: τ-functions and Virasoro constraints(Journal of mathematical physics, 2006) Martínez Alonso, Luis; Medina Reus, Elena; Mañas Baena, Manuel EnriqueA 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.Item Towards a theory of differential constraints of a hydrodynamic hierarchy(Journal of nonlinear mathematical physics, 2003) Martínez Alonso, Luis; Shabat, A. B.We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.Item Quasiconformal mappings and solutions of the dispersionless KP hierarchy(Theoretical and mathematical physics, 2002) Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, ElenaA ∂¯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.Item From Ramond fermions to Lamé equations for orthogonal curvilinear coordinates(Physics letters B, 1998) Mañas Baena, Manuel Enrique; Martínez Alonso, LuisWe show how Ramond free neutral Fermi fields lead to a Ƭ-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 Ribaucour transformation.Item Genus-zero Whitham hierarchies in conformal-map dynamics(Physics letters B, 2006) Martínez Alonso, Luis; Medina Reus, ElenaA 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.Item Localized coherent structures of the Davey-Stewartson equation in the bilinear formalism(Journal of mathematical physics, 1992) Martínez Alonso, Luis; Medina Reus, ElenaThe 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.Item The multicomponent 2D Toda hierarchy: dispersionless limit(Inverse problems, 2009) Mañas Baena, Manuel Enrique; Martínez Alonso, LuisThe 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 introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and Toda pictures of the dispersionless Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional symmetries and string equations for the dispersive Whitham hierarchy are studied in this limit.Item A classification of integrable quasiclassical deformations of algebraic curves(Journal of physics A: Mathematical and general, 2006) Konopelchenko, Boris; Martínez Alonso, Luis; Medina Reus, ElenaA 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.Item Regularization of Hele-Shaw flows, multiscaling expansions and the Painlevé I equation(Chaos solitons & Fractals, 2009) Martínez Alonso, Luis; Medina Reus, ElenaCritical 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.Item Spectral curves in gauge/string dualities: integrability, singular sectors and regularization.(Journal of physics A: Mathematical and theoretical, 2013) Konopelchenko, Boris; Martínez Alonso, Luis; Medina, ElenaWe 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 of the Whitham equations is used to determine the spectral curves from their moduli. An alternative characterization of the spectral curves in terms of critical points of a family of polynomial solutions W to Euler-Poisson-Darboux equations is provided. The equations for these critical points are a generalization of the planar limit equations for one-cut random matrix models. Moreover, singular spectral curves with higher order branch points turn out to be described by degenerate critical points of W. As a consequence we propose a multiple scaling limit method of regularization and show that, in the simplest cases, it leads to the Painlevè-I equation and its multi-component generalizations.