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An invariance analysis of the Vakhnenko–Parkes Equation

Author

Listed:
  • Hussain, Akhtar
  • Kara, A.H.
  • Zaman, F.D.

Abstract

Lie symmetry analysis of differential equations is an effective technique to compute exact solutions of a differential equation, to reduce number of independent variables or to reduce the order and nonlinearity of the equation. The present article focuses on the symmetry analysis of Vakhnenko–Parkes Equation (VP Equation). At first, Lie point symmetries of the VP Equation that permit an optimal system of one-dimensional subalgebras are discussed and then using the commutator table we construct the discrete symmetries of the VP Equation using the modified Hydon’s method. Also, we compute the exact solutions using symmetry transformations.

Suggested Citation

  • Hussain, Akhtar & Kara, A.H. & Zaman, F.D., 2023. "An invariance analysis of the Vakhnenko–Parkes Equation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003247
    DOI: 10.1016/j.chaos.2023.113423
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    References listed on IDEAS

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    1. V. O. Vakhnenko & E. J. Parkes, 2016. "Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-39, February.
    2. Hongwei Yang & Yunlong Shi & Baoshu Yin & Huanhe Dong, 2012. "Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-15, September.
    3. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
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