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

Author:

Niu Zhenjie,Li Biao

Abstract

AbstractThe 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.

Funder

National Natural Science Foundation of China

K. C. Wong Magna Fund in Ningbo University

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference32 articles.

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