Whitham systems and deformations

Details Whitham systems and deformations Whitham systems and deformations

2005-09-19

arxiv.org/abs/nlin/0509033v5

Journ. Math. Phys. 47, 073505 (2006)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, Latex

Scientific paper

10.1063/1.2217648

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.

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