Recursion operators of some equations of hydrodynamic type

Abstract

We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N = 2 and N = 3 containing the equations of shallow water waves and its generalizations with their first two general symmetries and their recursion operators. We also discuss a reduction of N+ 1 systems to TV systems of some new equations of hydrodynamic type. © 2001 American Institute of Physics.