NONCLASSICAL SYMMETRY REDUCTIONS OF THE CALOGERO-DEGASPERIS-FOKAS EQUATION IN (2+1) DIMENSIONS

摘要

In this paper we consider a (2 + 1)-dimensional integrable Calogero-Degasperis-Fokas equation. We apply the nonclassical method in order to obtain new symmetry reductions. From these partial differential equations in (1 + 1) dimensions by further reductions, we get second order ordinary differential equations. These ODE's provide several new solutions; all of them are expressible in terms of known functions, some of them are expressible in terms of the third Painleve trascendents. The corresponding solutions of the (2 + 1)-dimensional equation, involve up to three arbitrary smooth functions. Consequently the solutions exhibit a rich variety of qualitative behaviour.