Jacobi-elliptic Function, Trigonometric and Hyperbolic Soliton Solutions of the Combined Kairat-II-X Equation using the Kumar-Malik approach

• Shafiq Ahmad ^[1] ; Aman Ullah ^[1] ; Meraj Ali Khan ^[3] ; Shabir Ahmad ^[2]
  1. [1] University of Malakand

     University of Malakand

     Pakistán

     
  2. [2] Second University of Naples

     Second University of Naples

     Caserta, Italia

     
  3. [3] Imam Mohammad Ibn Saud Islamic University (IMSIU)

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
• Idioma: inglés
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• Resumen

  • The (1+1)-dimensional combined Kairat-II-X equation plays a crucial role in various physical systems, including hydrodynamic wave disturbances, plasma physics, and nonlinear optics. The aims of the current study is to discover some more soliton solutions for the (1+1)-dimensional combined Kairat-II-X equation, as these solutions offer important mathematical insights into wave dynamics. We employ a recently proposed Kumar-Malik method to derive soliton solutions for the (1+1)-dimensional combined Kairat-II-X equation. Using this approach, we derive several soliton solutions for the combined Kairat-II-X equation in (1+1) dimensions, encompassing Jacobi elliptic functions, hyperbolic functions, trigonometric functions, and exponential function solutions. The obtained solutions are then illustrated using 3D and contour plots to showcase the wave responses to changes in parameter values. The graphical demonstrations of some solutions give w-shaped, M-shaped, bright and dark soliton shaped for various values of parameters. To the best of our knowledge these solutions have not been studied before for the (1+1)-dimensional combined Kairat-II-X equation.

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