Bäcklund Transformations, Solitary Waves, Conoid Waves and Bessel Waves of the (2+1)-Dimensional Euler equation

Abstract

Some simple special Backlund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation.