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Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation

Author

Listed:
  • Tahir Ayaz
  • Farhad Ali
  • Wali Khan Mashwani
  • Israr Ali Khan
  • Zabidin Salleh
  • Ikramullah
  • Zakia Hammouch

Abstract

The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.

Suggested Citation

  • Tahir Ayaz & Farhad Ali & Wali Khan Mashwani & Israr Ali Khan & Zabidin Salleh & Ikramullah & Zakia Hammouch, 2021. "Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, June.
    • Handle: RePEc:hin:jjmath:7710333
    DOI: 10.1155/2021/7710333
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