Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient...

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.