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Dynamical Behavior and Wave Speed Perturbations in the (2 + 1) pKP Equation

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Abstract

The unidirectional propagation of long waves in certain nonlinear dispersive waves is explained by the (2 + 1) pKP equation, this equation admits infinite number of infinitesimals. We explored new Lie vectors thorough the commutative product properties. Using the Lie reduction stages and some assistant methods to solve the reduced ODEs, Exploiting a set of new solutions. Exploring a set of non-singular local multipliers; generating a set of local conservation laws for the studied equation. The nonlocally related (PDE) systems are found. Four nonlocally related systems are discussed reveal twenty-one interesting closed form solutions for this equation. We investigate new various solitons solutions as one soliton, many soliton waves move together, two and three Lump soliton solutions. Though three dimensions plots some selected solutions are plotted.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wen-Xiu Ma

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL33620-5700, USA

    Wen-Xiu Ma

  4. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Wen-Xiu Ma

  5. Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    Enas Y. Abu El Seoud & R. Sadat

  6. Faculty of Engineering and Technology, Future University, Cairo, Egypt

    Mohamed R. Ali

  7. Basic Engineering Mathematics Department, Benha Faculty of Engineering, Benha University, Benha, Egypt

    Mohamed R. Ali

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  1. Wen-Xiu Ma
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  2. Enas Y. Abu El Seoud
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  3. Mohamed R. Ali
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  4. R. Sadat
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Correspondence to Mohamed R. Ali.

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Ma, WX., Seoud, E.Y.A.E., Ali, M.R. et al. Dynamical Behavior and Wave Speed Perturbations in the (2 + 1) pKP Equation. Qual. Theory Dyn. Syst. 22, 2 (2023). https://doi.org/10.1007/s12346-022-00683-x

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  • DOI: https://doi.org/10.1007/s12346-022-00683-x

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