A family of (2+1)-dimensional hydrodynamic type systems possessing a pseudopotential

Abstract.

We construct a family of integrable hydrodynamic type systems with three independent and n ≥ 2 dependent variables in terms of solutions of a linear system of PDEs with rational coefficients. We choose the existence of a pseudopotential as a criterion of integrability. In the case n = 2 this family is a general solution of the classification problem for such systems. We also give an elliptic analog of this family in the case n > 2.