Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid

Abstract

Plasmas and fluids are of current interest, supporting a variety of wave phenomena. Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation for the nonlinear phenomena in a plasma or fluid. Based on the existing bilinear form, N -soliton solutions in the Gramian are derived, where N = 1, 2, 3…. With N = 3, three-soliton solutions are constructed. Fission and fusion for the three solitons are presented. Effects of the variable coefficients, i.e. h ( t ), l ( t ), q ( t ), n ( t ) and m ( t ), on the soliton fission and fusion are revealed: soliton velocity is related to h ( t ), l ( t ), q ( t ), n ( t ) and m ( t ), while the soliton amplitude cannot be affected by them, where t is the scaled temporal coordinate, h ( t ), l ( t ) and q ( t ) give the perturbed effects, and m ( t ) and n ( t ), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.

On the study of the higher-order and multiple lump/rogue waves to the (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation

“…Lump, lump-soliton and rouge-soliton solutions have been achieved [35]. N -soliton solutions in the Gramian have been obtained [36].…”