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A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions

Author

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  • Ruijuan Li

    (School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China)

  • Onur Alp İlhan

    (Department of Mathematics, Faculty of Education, Erciyes University, Melikgazi, Kayseri 38039, Turkey)

  • Jalil Manafian

    (Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov Str., Lankaran AZ4200, Azerbaijan)

  • Khaled H. Mahmoud

    (Department of Physics, College of Khurma University College, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mostafa Abotaleb

    (Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia)

  • Ammar Kadi

    (Department of Food and Biotechnology, South Ural State University, 454080 Chelyabinsk, Russia)

Abstract

In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rational solutions by selecting the interaction between a lump and one- or two-soliton solutions are obtained. The bilinear form is considered in terms of Hirota derivatives. Accordingly, the logarithm algorithm to obtain the exact solutions of a (3+1)-dimensional variable-coefficient (VC) generalized shallow water wave equation is utilized. The analytical treatment of extended homoclinic breather wave solutions is studied and plotted in three forms 3D, 2D, and density plots. Using suitable mathematical assumptions, the established solutions are included in view of a combination of two periodic and two solitons in terms of two trigonometric and two hyperbolic functions for the governing equation. Maple software for computing the complicated calculations of nonlinear algebra equations is used. The effect of the free parameters on the behavior of acquired figures to a few obtained solutions for two nonlinear rational exact cases was also discussed.

Suggested Citation

  • Ruijuan Li & Onur Alp İlhan & Jalil Manafian & Khaled H. Mahmoud & Mostafa Abotaleb & Ammar Kadi, 2022. "A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions," Mathematics, MDPI, vol. 10(17), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3074-:d:898180
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    References listed on IDEAS

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    1. Fanwei Meng & Dini Wang & Penghui Yang & Guanzhou Xie, 2019. "Application of Sum of Squares Method in Nonlinear H ∞ Control for Satellite Attitude Maneuvers," Complexity, Hindawi, vol. 2019, pages 1-10, November.
    2. Chen, Yiren & Liu, Rui, 2015. "Some new nonlinear wave solutions for two (3+1)-dimensional equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 397-411.
    3. Yuefeng Zhou & Chuanjian Wang & Xiaoxue Zhang, 2020. "Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    4. Abdulmohsen D. Alruwaili & Aly R. Seadawy & Syed T. R. Rizvi & Sid Ahmed O. Beinane, 2022. "Diverse Multiple Lump Analytical Solutions for Ion Sound and Langmuir Waves," Mathematics, MDPI, vol. 10(2), pages 1-21, January.
    5. Sijia Chen & Jian Zhang & Fanwei Meng & Dini Wang & Wei Zhang, 2021. "A Markov Chain Position Prediction Model Based on Multidimensional Correction," Complexity, Hindawi, vol. 2021, pages 1-8, January.
    6. Aly R. Seadawy & Hanadi Zahed & Syed T. R. Rizvi, 2022. "Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
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    Cited by:

    1. Shami A. M. Alsallami & Syed T. R. Rizvi & Aly R. Seadawy, 2023. "Study of Stochastic–Fractional Drinfel’d–Sokolov–Wilson Equation for M-Shaped Rational, Homoclinic Breather, Periodic and Kink-Cross Rational Solutions," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    2. Liu, Yaqing & Peng, Linyu, 2023. "Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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