On the Liouville Integrable Reduction of the Associativity Equations in the Case of Three Primary Fields

Abstract

In this paper, a canonical Hamiltonian reduction of the associativity equations with the antidiagonal matrix η i j \eta _{ij} in the case of three primary fields is constructed explicitly, and its Liouville integrability is proved. Moreover, for the considered associativity equations a first integral of the second order is found explicitly and an infinite family of first integrals is investigated.