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

Journal of Mathematical Physics
 Pub Date:
 July 2006
 DOI:
 10.1063/1.2217648
 arXiv:
 arXiv:nlin/0509033
 Bibcode:
 2006JMP....47g3505M
 Keywords:

 02.30.Rz;
 02.60.Nm;
 Integral equations;
 Integral and integrodifferential equations;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 27 pages, Latex