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Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves

Author

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  • Sumayah Hamzah Alhejaili

    (Department of Mathematics, College of Science, Taibah University, Al-Madinah al-Munawwarah 42353, Saudi Arabia)

  • Abdulghani Alharbi

    (Department of Mathematics, College of Science, Taibah University, Al-Madinah al-Munawwarah 42353, Saudi Arabia)

Abstract

In this article, we successfully obtain novel solutions for the coupled Drinfel’d–Sokolov–Wilson DSW system utilizing various methods. These include soliton solutions characterized by hyperbolic, rational, and trigonometric functions. Specifically, the generalized exponential rational function method (GERFM) and a modified version of the new Kudryashov method (MVNK) are employed to derive diverse soliton solutions for the system. Additionally, we demonstrate numerical solutions for the coupled Drinfel’d–Sokolov–Wilson system using adaptive moving mesh and uniform mesh methods. Also, we study the stability and error analysis of the numerical schemes. To validate the accuracy and reliability of the exact solutions obtained through analytical methods, we compare them with the numerical solutions both analytically and graphically. The techniques presented in this article are deemed suitable and acceptable and can be effectively applied to solve other nonlinear evolution systems.

Suggested Citation

  • Sumayah Hamzah Alhejaili & Abdulghani Alharbi, 2023. "Structure of Analytical and Numerical Wave Solutions for the Nonlinear (1 + 1)-Coupled Drinfel’d–Sokolov–Wilson System Arising in Shallow Water Waves," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4598-:d:1277279
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