Multi-component Toda lattice hierarchy

Abstract

We give a detailed account of the N -component Toda lattice hierarchy. This hierarchy is an extended version of the one introduced by Ueno and Takasaki. Our version contains N discrete variables rather than one. We start from the Lax formalism, deduce the bilinear relation for the wave functions from it and then, based on the latter, prove existence of the tau-function. We also show how the multi-component Toda lattice hierarchy is embedded into the universal hierarchy which is basically the multi-component KP hierarchy. At last, we show how the bilinear integral equation for the tau-function can be obtained using the free fermion technique. An example of exact solutions (a multi-component analogue of one-soliton solutions) is given.

68 pages, no figure; rev. 72 pages, no figure (introduction extended); 2nd rev. 72 pages (several references added, typos corrected)

References in corpus (6)

• Integrable Hierarchies and Dispersionless Limit
• W-Geometries
• Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
• The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations
• Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model
• Toda lattice with constraint of type B