New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation

Abstract

In this paper, we mainly pay attention to prove the existence of lump solutions to a generalized (3+1)-dimensional nonlinear differential equation. Hirota's bilinear method and a quadratic function method are employed to derive the lump solutions localized in the whole plane for a (3+1)-dimensional nonlinear differential equation. Three examples of such nonlinear equation are presented to investigate the exact expressions of the lump solutions. Moreover, the 3d plots and corresponding density plots of the solutions are given to show the space structures of the lump waves. In addition, the breath-wave solutions and several interaction solutions of the (3+1)-dimensional nonlinear differential equation are obtained and their dynamics are analyzed.

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

“…Using both the Hirota bilinear method and the quadratic function method, Zhou et al derived the lump solutions of the variable-coefficient (3+1)dimensional generalized Calogero-Bogoyavlenskii-Schif equation [28]. Based on the same approach [27], the lump solutions are given in a more generalized variable-coefficient (3+1)-dimensional nonlinear differential equation [29]. Utilizing the Bäcklund transformation, the lump solutions and some novel interactional solutions are discussed in a high-dimensional nonlinear system [30].…”