Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system

Riadh Chteoui; Abdulrahman F. Aljohani; Anouar Ben Mabrouk; Riadh Chteoui; Abdulrahman F. Aljohani; Anouar Ben Mabrouk

doi:10.3934/era.2021002

Electronic Research Archive

2021, Volume 29, Issue 4: 2561-2597. doi: 10.3934/era.2021002

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Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system

1.
Department of Mathematics, Faculty of Sciences, University of Tabuk, Saudi Arabia, Lab. of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics
2.
Faculty of Sciences, University of Monastir, 5000 Monastir, Tunisia
3.
Department of Mathematics, Faculty of Sciences, University of Tabuk, Saudi Arabia
4.
Department of Mathematics, Higher Institute of Applied Mathematics and Computer, Science, University of Kairouan, Street of Assad Ibn Alfourat, 3100 Kairouan, Tunisia, Lab. of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics
5.
Department of Mathematics, Faculty of Sciences, University of Tabuk, Saudi Arabia

Received: 01 August 2020 Revised: 01 November 2020 Published: 11 January 2021
Primary: 35Q41, 35J50; Secondary: 35J10, 35Q55

In this paper, we study a couple of NLS equations characterized by mixed cubic and super-linear sub-cubic power laws. Classification as well as existence and uniqueness of the steady state solutions have been investigated. Numerical simulations have been also provided illustrating graphically the theoretical results. Such simulations showed that possible chaotic behaviour seems to occur and needs more investigations.
- Variational,
- energy functional,
- existence,
- uniqueness,
- NLS system,
- classification,
- chaotic,
- simulation
Citation: Riadh Chteoui, Abdulrahman F. Aljohani, Anouar Ben Mabrouk. Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system[J]. Electronic Research Archive, 2021, 29(4): 2561-2597. doi: 10.3934/era.2021002

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Abstract

In this paper, we study a couple of NLS equations characterized by mixed cubic and super-linear sub-cubic power laws. Classification as well as existence and uniqueness of the steady state solutions have been investigated. Numerical simulations have been also provided illustrating graphically the theoretical results. Such simulations showed that possible chaotic behaviour seems to occur and needs more investigations.

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