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Lyapunov–Sylvester computational method for numerical solutions of a mixed cubic-superlinear Schrödinger system

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Abstract

In this paper a nonlinear coupled Schrödinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea consists in transforming the continuous system into an algebraic quasi linear dynamical discrete one leading to generalized semi-linear operators. Next, the discrete algebraic system is studied for solvability, stability and convergence. At the final step, numerical examples are provided to illustrate the efficiency of the theoretical results.

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Authors and Affiliations

  1. LR15ES18 Algebra, Number Theory and Nonlinear Analysis Lab, Department of Mathematics, Faculty of Sciences, University of Monastir, 5000, Monastir, Tunisia

    Riadh Chteoui & Anouar Ben Mabrouk

  2. Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk, Saudi Arabia

    Riadh Chteoui, Abdulrahman F. Aljohani & Anouar Ben Mabrouk

  3. Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, 3100, Kairouan, Tunisia

    Anouar Ben Mabrouk

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  1. Riadh Chteoui
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  2. Abdulrahman F. Aljohani
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  3. Anouar Ben Mabrouk
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Correspondence to Anouar Ben Mabrouk.

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Chteoui, R., Aljohani, A.F. & Ben Mabrouk, A. Lyapunov–Sylvester computational method for numerical solutions of a mixed cubic-superlinear Schrödinger system. Engineering with Computers 38 (Suppl 2), 1081–1094 (2022). https://doi.org/10.1007/s00366-020-01264-9

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  • DOI: https://doi.org/10.1007/s00366-020-01264-9

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