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M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model

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  • He, Xue-Jiao
  • Lü, Xing

Abstract

In the previous study, the one-lump solution is given to the dimensionally reduced forms of a (3+1)-dimensional nonlinear model via the positive quadratic function method. The main work of this paper is to construct the M-lump solution and the Wronskian solution to this (3+1)-dimensional nonlinear model. Firstly, the M-lump solution is constructed by using the long wave limit method. As an example, the three-dimensional plots of one-, two- and three-lump solutions and the corresponding density plots have been shown through selecting appropriate parameters. What is more, their motion process is analyzed systematically. Secondly, a sufficient condition of Wronskian solution is given by using the properties of determinant and Plücker relation. Based on the Wronskian form, we obtain the soliton solution and the rational solution by selecting the elements in the determinant which satisfy the linear partial differential systems. Finally, several specific examples are presented.

Suggested Citation

  • He, Xue-Jiao & Lü, Xing, 2022. "M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 327-340.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:327-340
    DOI: 10.1016/j.matcom.2022.02.014
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Iqbal, Mujahid & Lu, Dianchen, 2020. "Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
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    Cited by:

    1. Cao, Na & Yin, XiaoJun & Bai, ShuTing & LiYangXu,, 2023. "Breather wave, lump type and interaction solutions for a high dimensional evolution model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Chen, Si-Jia & Lü, Xing, 2022. "Observation of resonant solitons and associated integrable properties for nonlinear waves," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Wang, Xiaoning & Liu, Minzhuang & Ci, Yusheng & Wu, Lina, 2022. "Effect of front two adjacent vehicles’ velocity information on car-following model construction and stability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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