Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
| dc.creator | Takasaki, Kanehisa | |
| dc.creator | Takebe, Takashi | |
| dc.date | 2006-08-31 | |
| dc.date | 2007-08-31 | |
| dc.date.accessioned | 2026-07-07T11:07:22Z | |
| dc.date.available | 2026-07-07T11:07:22Z | |
| dc.description | 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 $τ$-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 $S$-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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/nlin/0608068 | |
| dc.identifier | http://arxiv.org/abs/nlin/0608068 | |
| dc.identifier | PhysicaD235:109-125,2007 | |
| dc.identifier | doi:10.1016/j.physd.2007.04.017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/189820 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy | |
| dc.type | text |