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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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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.texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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 [...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
The dispersionless limit of the scalar nonlocal a-problem is derived. It is given by a special class of nonlinear first-order equations. A quasiclassical version of the partial derivative -dressing method is presented. It is shown that the algeb[...]texto impreso
A systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay's identities an obtained. It is shown that in terms of these variabl[...]
