Bar{partial }-Dressing Method for a Generalized (2 + 1)-Dimensional Nonlinear Wave Equation

Abstract

The main purpose of this work is solving a generalized (2 + 1)-dimensional nonlinear wave equation via bar{partial }-dressing method. The key to this process is to establish connection between characteristic functions and bar{partial }-problem. With use of Fourier transformation and Fourier inverse transformation, we obtain explicit expressions of Green’s function and give two characteristic functions corresponding to general potential. Further, the bar{partial }-problem is constructed by calculating bar{partial } derivative of characteristic function. The solution of bar{partial }-problem can be shown by Cauchy–Green formula, and after determining time evolution of scatter data, we can give solutions of the (2 + 1)-dimensional equation.