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Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations

Author

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  • Aly R. Seadawy

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

  • Syed T. R. Rizvi

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad 45550, Pakistan)

  • Hanadi Zahed

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

Abstract

This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions.

Suggested Citation

  • Aly R. Seadawy & Syed T. R. Rizvi & Hanadi Zahed, 2023. "Lump-Type Solutions, Lump Solutions, and Mixed Rogue Waves for Coupled Nonlinear Generalized Zakharov Equations," Mathematics, MDPI, vol. 11(13), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2856-:d:1179387
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. R. Soundararajan & V. Subburayan & Patricia J. Y. Wong, 2023. "Streamline Diffusion Finite Element Method for Singularly Perturbed 1D-Parabolic Convection Diffusion Differential Equations with Line Discontinuous Source," Mathematics, MDPI, vol. 11(9), pages 1-17, April.
    3. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Zhang, Weiguo & Feng, Liping & Chang, Qianshun, 2007. "Conditional stability of solitary-wave solutions for generalized Boussinesq equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1108-1117.
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