Symmetry in Nonlinear Mathematical Physics - 2009
Maxim Pavlov (P.N. Lebedev Physical Institute, Moscow, Russia)
Integrability of generalized Boyer-Finley system
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.