On Associativity Equations in Dispersionless Integrable Hierarchies
High Energy Physics - Theory
2009-11-07 v2 Exactly Solvable and Integrable Systems
Abstract
We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda hierarchies. We show, therefore, that any tau-function of dispersionless KP or Toda hierarchy provides a solution to associativity equations. In general, they depend on infinitely many variables. We also discuss the particular solution to the dispersionless Toda hierarchy that describes conformal mappings and construct a family of new solutions to the WDVV equations depending on finite number of variables.
Cite
@article{arxiv.hep-th/0105260,
title = {On Associativity Equations in Dispersionless Integrable Hierarchies},
author = {A. Boyarsky and A. Marshakov and O. Ruchayskiy and P. Wiegmann and A. Zabrodin},
journal= {arXiv preprint arXiv:hep-th/0105260},
year = {2009}
}
Comments
16 pages, LaTeX