Exact solutions of a (3+1)-dimensional nonlinear evolution equation based on its Wronskian form

Abstract

In this paper, the Hirota bilinear method is applied to investigate the exact solutions of a (3+1)-dimensional nonlinear evolution equation. The soliton, breather and lump solutions satisfying specific Wronskian conditions are obtained. Especially, starting from the 2Mth-order Wronskian determinant solution, we obtain the determinant expression of arbitrary Mth-order lump solution through the elementary transformation and long wave limit method. Some images are used as examples to illustrate their dynamics. These results can be helpful to understand the propagation processes of nonlinear waves in some nonlinear physical systems, such as fluid mechanics, nonlinear optics and so on.

Keywords

• (3+1)-dimensional nonlinear evolution equation
• Hirota bilinear method
• Wronskian form
• Exact solutions