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Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

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  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
    Material Science Innovation and Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa)

Abstract

This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear model. A line of critical points of the lump waves is computed, whose two spatial coordinates travel at constant speeds. The corresponding maximum and minimum values are evaluated in terms of the wave numbers, and interestingly, all those extreme values do not change with time, either. The last section is the conclusion.

Suggested Citation

  • Wen-Xiu Ma, 2023. "Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions," Mathematics, MDPI, vol. 11(22), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4664-:d:1281536
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    References listed on IDEAS

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    1. Xu, Xi-Xiang, 2015. "A deformed reduced semi-discrete Kaup–Newell equation, the related integrable family and Darboux transformation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 275-283.
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    Cited by:

    1. Li, Zitian, 2024. "New coherent structures and interaction behavior for the new (2+1)-dimensional Korteweg-de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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