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Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method

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  • Feiyun Pei

    (School of Economics and Management, Huainan Normal University, Huainan 232038, China)

  • Guojiang Wu

    (Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

  • Yong Guo

    (Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

Abstract

The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear optics, and other fields. In the process of studying these topics, it is very important to obtain the exact solutions of the KPI equation. In this paper, a general Riccati equation is treated as an auxiliary equation, which is solved to obtain many new types of solutions through several different function transformations. We solve the KPI equation using this general Riccati equation, and construct ten sets of the infinite series exact solitary wave solution of the KPI equation. The results show that this method is simple and effective for the construction of infinite series solutions of nonlinear evolution models.

Suggested Citation

  • Feiyun Pei & Guojiang Wu & Yong Guo, 2023. "Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1560-:d:1104728
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    References listed on IDEAS

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    1. Xiaomeng Zhu & Jinkang Cheng & Zhuokai Chen & Guojiang Wu, 2022. "New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    2. Abdou, M.A., 2007. "The extended F-expansion method and its application for a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 95-104.
    3. Seadawy, Aly R. & Lu, Dianchen & Nasreen, Naila & Nasreen, Shamila, 2019. "Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    4. Valentine Aleksandrovich Kim & Roman Ivanovich Parovik & Zafar Ravshanovich Rakhmonov, 2023. "Implicit Finite-Difference Scheme for a Duffing Oscillator with a Derivative of Variable Fractional Order of the Riemann-Liouville Type," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
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    Cited by:

    1. Yuli D. Chashechkin & Artem A. Ochirov, 2023. "Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field," Mathematics, MDPI, vol. 11(21), pages 1-18, October.

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