M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model

Xue-Jiao He and Xing Lü

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 197, issue C, 327-340

Abstract: In the previous study, the one-lump solution is given to the dimensionally reduced forms of a (3+1)-dimensional nonlinear model via the positive quadratic function method. The main work of this paper is to construct the M-lump solution and the Wronskian solution to this (3+1)-dimensional nonlinear model. Firstly, the M-lump solution is constructed by using the long wave limit method. As an example, the three-dimensional plots of one-, two- and three-lump solutions and the corresponding density plots have been shown through selecting appropriate parameters. What is more, their motion process is analyzed systematically. Secondly, a sufficient condition of Wronskian solution is given by using the properties of determinant and Plücker relation. Based on the Wronskian form, we obtain the soliton solution and the rational solution by selecting the elements in the determinant which satisfy the linear partial differential systems. Finally, several specific examples are presented.

Keywords: M-lump solution; Soliton solution; Rational solution; (3+1)-dimensional nonlinear equation; Wronskian solution (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:197:y:2022:i:c:p:327-340

DOI: 10.1016/j.matcom.2022.02.014

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