Integrability of generalized Boyer-Finley system

Abstract:
We consider a new four component three-dimensional hydrodynamic type system, which is two-component reduction is nothing but the remarkable Boyer-Finley equation (also known as a continuum limit of two-dimensional Toda Lattice). In this case, infinitely many N component hydrodynamic reductions parameterized by 2N arbitrary functions of a single variable are found. Their general solutions given by generalized hodograph transform are paramerized by N functions of a single variable.