Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory (Q1305719)

The problem of classification of compatible Poisson structures of hydrodynamic type, i.e. compatible local first-order homogeneous Poisson brackets in field theory is studied. The author shows that all two-component compatible Poisson structures of hydrodynamic type are classified by means of the solutions of a homogeneous four-component system of hydrodynamic type. He proves that the two-component reduction of this system is related to the equations of associativity in two-dimensional topological field theory. It is also true in the case of deformations of two special Frobenius algebras.