Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

Abstract

Using the idea of transformation, some links between (2+1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev–Petviashvili (KP) equation, generalized (2+1)-dimensional break soliton equation and (2+1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2+1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.