Associativity equations in dispersionless integrable hierarchies

A. Boyarsky, A. Marshakov, O. Ruchayskiy, P. Wiegmann, A. Zabrodin

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)483-492
Number of pages10
JournalPhysics Letters B
Issue number3-4
Publication statusPublished - 30 Aug 2001
Externally publishedYes


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