The Extended Toda Hierarchy

By Guido Carlet, Boris Dubrovin, You-jin Zhang. Moscow Mathematical Journal, 2003

168 citations recorded by the source corpus.

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

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f8e94ed667a04eede8da51e46921ee9e5590cf13

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Classical Hurwitz numbers and related combinatorics (2016, background): “This would suggest a new and geometric proof of the Toda conjecture [42], [19], [7] for the GW invariants of P(1) in the stationary sector.”
Gromov-Witten theory, Hurwitz theory, and completed cycles (2002, unknown): “Further clariﬁcation of the structure of the extended Toda hierarchy was obtained by Carlet, Dubrovin, and Zhang in [3].”
Hirota quadratic equations for the extended Toda hierarchy (2005, methodology): “als in τ(x) and its partial derivatives). The regularity condition in (1.1) means, by deﬁnition, that all the Laurent series in λ−1 are polynomials in λ. We describe the Lax form of the ETH following [CDZ] 1. Introduce a Lax operator (1.2) L = Λ+u+QevΛ−1, 1In the papers [Ge, Z] the ETH is deﬁned imp”