The Extended Toda Hierarchy

Details The Extended Toda Hierarchy The Extended Toda Hierarchy

2003-06-29

arxiv.org/abs/nlin/0306060v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

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 $CP^1$ topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schr\"odinger hierarchy.

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