New lump solutions of the (3+1)-dimensional generalized Camassa–Holm Kadomtsev–Petviashvili (gCH-KP) equation

Abstract

In this paper, we investigate lump solutions of the (3+1)-dimensional gCH-KP equation employing the Hirota’s bilinear method and symbolic computation method. The bilinear form of the equation is first derived via the Hirota’s bilinear method under the appropriate transformations. Based on the bilinear form, some new 1-lump, 2-lump, 3-lump and 6-lump solutions of the (3+1)-dimensional gCH-KP equation are obtained with aid of the Maple via the symbolic computation method. The lump solutions are also illustrated by two-dimensional, three-dimensional and contour plots. The results obtained in this paper will be used to describe some interesting nature phenomena in the physics, oceanography, gas dynamics, biophysics, nonlinear optics and so on.

Keywords

• (3+1)-dimensional gCH-KP equation
• Hirota’s bilinear method
• Symbolic computation
• Lump solution