Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
Abstract
The goal of this paper is to identify the universal Whitham hierarchy of genus zero with a dispersionless limit of the multi-component KP hierarchy. To this end, the multi-component KP hierarchy is (re)formulated to depend on several discrete variables called ``charges''. These discrete variables play the role of lattice coordinates in underlying Toda field equations. A multi-component version of the so called differential Fay identity are derived from the Hirota equations of the -function of this ``charged'' multi-component KP hierarchy. These multi-component differential Fay identities have a well-defined dispersionless limit (the dispersionless Hirota equations). The dispersionless Hirota equations turn out to be equivalent to the Hamilton-Jacobi equations for the -functions of the universal Whitham hierarchy. The differential Fay identities themselves are shown to be a generating functional expression of auxiliary linear equations for scalar-valued wave functions of the multi-component KP hierarchy.
Keywords
Cite
@article{arxiv.nlin/0608068,
title = {Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy},
author = {Kanehisa Takasaki and Takashi Takebe},
journal= {arXiv preprint arXiv:nlin/0608068},
year = {2008}
}
Comments
latex2e (a4paper, 12pt) using packages "amssymb,amsmath,amsthm", 44 pages, no figure; (v2) a few typos corrected, bibliographic data updated, final form for publication in special issue of Physica D (2007)