The Extended Toda Hierarchy

Abstract

We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the $C{P}^1$ topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schrödinger hierarchy.

23 pages, a remark at the end of Section 4 added

Cited by in corpus (1)

• Methods of geometry of differential equations in analysis of the integrable field theory models