Dynamical behaviors to the coupled Schrödinger-Boussinesq system with the beta derivative

Hajar F. Ismael; Hasan Bulut; Haci Mehmet Baskonus; Wei Gao; Hajar F. Ismael; Hasan Bulut; Haci Mehmet Baskonus; Wei Gao

doi:10.3934/math.2021459

AIMS Mathematics

2021, Volume 6, Issue 7: 7909-7928. doi: 10.3934/math.2021459

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Research article

Dynamical behaviors to the coupled Schrödinger-Boussinesq system with the beta derivative

1.
Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq
2.
Department of Mathematics, Faculty of Science, Firat University, Elazig, Turkey
3.
Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey
4.
School of information Science and Technology, Yunnan Normal University, Yunnan, China

Received: 22 March 2021 Accepted: 30 April 2021 Published: 19 May 2021
MSC : 35Q41, 35Q60

In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrödinger-Boussinesq system that includes beta derivative. The new exact solution is obtained have a hyperbolic function, trigonometric function, exponential function, and rational function. These solutions might appreciate in laser and plasma sciences. It is shown that this method, provides a straightforward and powerful mathematical tool for solving the nonlinear problems. Moreover, the linear stability of this nonlinear system is analyzed.
- Schrödinger-Boussinesq system,
- beta derivative,
- modulation instability analysis
Citation: Hajar F. Ismael, Hasan Bulut, Haci Mehmet Baskonus, Wei Gao. Dynamical behaviors to the coupled Schrödinger-Boussinesq system with the beta derivative[J]. AIMS Mathematics, 2021, 6(7): 7909-7928. doi: 10.3934/math.2021459

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Abstract

In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrödinger-Boussinesq system that includes beta derivative. The new exact solution is obtained have a hyperbolic function, trigonometric function, exponential function, and rational function. These solutions might appreciate in laser and plasma sciences. It is shown that this method, provides a straightforward and powerful mathematical tool for solving the nonlinear problems. Moreover, the linear stability of this nonlinear system is analyzed.

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