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Research Article | Open Access

Soliton solutions and periodic solutions for two models arises in mathematical physics

F. A. Mohammed1,2( ), Mohammed K. Elboree2
Department of mathematics, College of Science and Arts, Jouf university, Al-Gurayat, Kingdom of Saudi Arabia
Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt
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Abstract

We aimed in this paper to acquire the periodic wave solutions and soliton solutions and other solutions such as kink-wave solutions for the cubic nonlinear Schrödinger equation with repulsive delta potential ( δ-NLSE) and complex coupled Higgs field equation via two mathematical methods Jacobi elliptic function method and generalized Kudryashov method. Some of these solutions are degenerated to solitary wave solutions and periodic wave solutions in the limit case. We also gave the meaning of these solutions physically and the numerical simulation by some figures.

Keywords

cubic nonlinear Shrödinger's equation with repulsive delta potential equationcomplex coupled Higgs field equationJacobi elliptic function methodgeneralized Kudryashov methodperiodic solutionssoliton solutions
CLC number: 35Q51, 37K40, 35G20, 35Q60

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4439-4458
DOI: 10.3934/math.2022247

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Cite this article:
Mohammed FA, Elboree MK. Soliton solutions and periodic solutions for two models arises in mathematical physics. AIMS Mathematics, 2022, 7(3): 4439-4458. https://doi.org/10.3934/math.2022247

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Received: 21 October 2021
Revised: 09 December 2021
Accepted: 16 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)