Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid. (30th August 2019)

• Record Type: Journal Article
• Authors: Chen, Su-Su; Tian, Bo
• Is Part Of: Proceedings. Volume 475:Number 2228(2019)
• Publication Date: 2019-08-30
• Subjects: plasma -- fluid -- generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation -- N-soliton solutions in the Gramian -- soliton interaction; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2019.0122
• Languages: English
• ISSNs: 1364-5021

Abstract

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.