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Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves

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  • Sadat, R.
  • Saleh, R.
  • Kassem, M.
  • Mousa, Mohamed M.

Abstract

Using the algebraic approach Lie symmetries, we spin new infinitesimals for the (4+1) Fokas equation that admits an infinite number of possibilities for its Lie vectors. Through the commutation product between the unknown vectors, we generate a system of ordinary differential equations (ODEs). By solving this system, we explore these infinitesimals. Through four stages of the similarity reduction using double and triple combinations between the examined vectors, we explore new soliton solutions. These results are simulated through three and two-dimensional plots that illustrates the dynamical behavior of these solutions is presented for different values of the free valued function at different values of time. A comparison with other results is presented.

Suggested Citation

  • Sadat, R. & Saleh, R. & Kassem, M. & Mousa, Mohamed M., 2020. "Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305300
    DOI: 10.1016/j.chaos.2020.110134
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    References listed on IDEAS

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    1. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    2. R. Sadat & M. Kassem & Wen-Xiu Ma, 2018. "Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1) Dimensional Model," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-8, December.
    3. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    4. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    5. Sheng Zhang & Meitong Chen, 2015. "Painlevé Integrability and New Exact Solutions of the (4 + 1)-Dimensional Fokas Equation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, December.
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    Cited by:

    1. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Tanwar, Dig Vijay, 2022. "Lie symmetry reductions and generalized exact solutions of Date–Jimbo–Kashiwara–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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