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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, whereN  = 1, 2, 3…. WithN  = 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 ) andm (t ), on the soliton fission and fusion are revealed: soliton velocity is related toh (t ),l (t ),q (t ),n (t ) andm (t ), while the soliton amplitude cannot be affected by them, wheret is the scaled temporal coordinate,h (t ),l (t ) andq (t ) give the perturbed effects, andm (t ) andn (t ), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.

proceedings - royal society. mathematical, physical and engineering sciences

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