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Symmetry
Volume 13
Issue 2
10.3390/sym13020190
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Article

Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System

by
Riadh Chteoui
1,2,†,
Abdulrahman F. Aljohani
1,† and
Anouar Ben Mabrouk
1,2,3,*,†
1
Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia
2
Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, Monastir 5019, Tunisia
3
Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Street of Assad Ibn Alfourat, Kairouan 3100, Tunisia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2021, 13(2), 190; https://doi.org/10.3390/sym13020190
Submission received: 11 December 2020 / Revised: 9 January 2021 / Accepted: 13 January 2021 / Published: 26 January 2021
(This article belongs to the Special Issue Advanced Calculus in Problems with Symmetry)
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Abstract

Systems of coupled nonlinear PDEs are applied in many fields as suitable models for many natural and physical phenomena. This makes them active and attractive subjects for both theoretical and numerical investigations. In the present paper, a symmetric nonlinear Schrödinger (NLS) system is considered for the existence of the steady state solutions by applying a minimizing problem on some modified Nehari manifold. The nonlinear part is a mixture of cubic and superlinear nonlinearities and cubic correlations. Some numerical simulations are also illustrated graphically to confirm the theoretical results.
Keywords: steady states; variational methods; energy functional; existence of solutions; Nehari manifold; NLS systems steady states; variational methods; energy functional; existence of solutions; Nehari manifold; NLS systems

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MDPI and ACS Style

Chteoui, R.; Aljohani, A.F.; Ben Mabrouk, A. Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System. Symmetry 2021, 13, 190. https://doi.org/10.3390/sym13020190

AMA Style

Chteoui R, Aljohani AF, Ben Mabrouk A. Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System. Symmetry. 2021; 13(2):190. https://doi.org/10.3390/sym13020190

Chicago/Turabian Style

Chteoui, Riadh, Abdulrahman F. Aljohani, and Anouar Ben Mabrouk. 2021. "Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System" Symmetry 13, no. 2: 190. https://doi.org/10.3390/sym13020190

APA Style

Chteoui, R., Aljohani, A. F., & Ben Mabrouk, A. (2021). Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System. Symmetry, 13(2), 190. https://doi.org/10.3390/sym13020190

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