The WDVV Associativity Equations as a High-Frequency Limit

Abstract

International audienceIn this paper, we present a new “Hamiltonian” approach for construction of integrable systems. We found an intermediate dispersive system of a Camassa–Holm type. This three-component system has simultaneously a high-frequency (short wave) limit equivalent to the remarkable WDVV associativity equations and a dispersionless (long wave) limit coinciding with a dispersionless limit of the Yajima–Oikawa system