Whitham systems and deformations

Abstract

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius manifolds corresponding to the Whitham systems of integrable hierarchies. Under some non-degeneracy requirements we suggest a general scheme of the deformation of the hyperbolic Whitham systems using the initial non-linear system. The general form of the deformed Whitham system coincides with the form of the "low-dispersion" asymptotic expansions used by B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius manifolds.

27 pages, Latex

References in corpus (5)

• Deformations of Semisimple Bihamiltonian Structures of Hydrodynamic Type
• On Hamiltonian perturbations of hyperbolic systems of conservation laws
• Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type
• Extended affine Weyl groups and Frobenius manifolds -- II
• On the Quasitriviality of Deformations of Bihamiltonian Structures of Hydrodynamic Type

Cited by in corpus (7)

• Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
• The deformation of the Whitham systems in the almost linear case
• The deformations of Whitham systems and Lagrangian formalism
• On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations
• The multi-dimensional Hamiltonian Structures in the Whitham method
• The Lorentz - invariant deformation of the Whitham system for the non-linear Klein-Gordon equation
• The conservation of the Hamiltonian structures in the deformations of the Whitham systems