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

F. A. Mohammed; Mohammed K. Elboree; F. A. Mohammed; Mohammed K. Elboree

doi:10.3934/math.2022247

AIMS Mathematics

2022, Volume 7, Issue 3: 4439-4458. doi: 10.3934/math.2022247

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

F. A. Mohammed ^{1,2
,
,},
Mohammed K. Elboree ²

1.
Department of mathematics, College of Science and Arts, Jouf university, Al-Gurayat, Kingdom of Saudi Arabia
2.
Department of mathematics, Faculty of Science, South Valley University, Qena, Egypt

Received: 21 October 2021 Revised: 09 December 2021 Accepted: 16 December 2021 Published: 22 December 2021
MSC : 35Q51, 37K40, 35G20, 35Q60

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 ($ \delta $-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.
Citation: F. A. Mohammed, Mohammed K. Elboree. Soliton solutions and periodic solutions for two models arises in mathematical physics[J]. AIMS Mathematics, 2022, 7(3): 4439-4458. doi: 10.3934/math.2022247

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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 ($ \delta $-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.

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