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On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation

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  • Wang, Xiu-Bin
  • Tian, Shou-Fu
  • Xua, Mei-Juan
  • Zhang, Tian-Tian

Abstract

Under investigation in this paper is the integrability of a (3+1)-dimensional generalized KdV-like model equation, which can be reduced to several integrable equations. With help of Bell polynomials, an effective method is presented to succinctly derive the bilinear formalism of the equation, based on which, the soliton solutions and periodic wave solutions are also constructed by using Riemann theta function. Furthermore, the Bäcklund transformation, Lax pairs, and infinite conservation laws of the equation can easily be derived, respectively. Finally, the relationship between periodic wave solutions and soliton solutions are systematically established. It is straightforward to verify that these periodic waves tend to soliton solutions under a small amplitude limit.

Suggested Citation

  • Wang, Xiu-Bin & Tian, Shou-Fu & Xua, Mei-Juan & Zhang, Tian-Tian, 2016. "On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 216-233.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:216-233
    DOI: 10.1016/j.amc.2016.02.028
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    References listed on IDEAS

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    1. Tian, Shou-Fu & Zhang, Hong-Qing, 2013. "Riemann theta functions periodic wave solutions and rational characteristics for the (1+1)-dimensional and (2+1)-dimensional Ito equation," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 27-41.
    2. Tu, Jian-Min & Tian, Shou-Fu & Xu, Mei-Juan & Zhang, Tian-Tian, 2016. "On Lie symmetries, optimal systems and explicit solutions to the Kudryashov–Sinelshchikov equation," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 345-352.
    3. Kara, A.H. & Razborova, Polina & Biswas, Anjan, 2015. "Solitons and conservation laws of coupled Ostrovsky equation for internal waves," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 95-99.
    4. Kudryashov, Nikolay A. & Ryabov, Pavel N., 2014. "Exact solutions of one pattern formation model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1090-1093.
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    Cited by:

    1. Zheng-Yi Ma & Jin-Xi Fei & Jun-Chao Chen & Quan-Yong Zhu, 2019. "Resonant Soliton and Soliton-Cnoidal Wave Solutions for a (3+1)-Dimensional Korteweg-de Vries-Like Equation," Complexity, Hindawi, vol. 2019, pages 1-11, July.
    2. El-Dessoky, M.M. & Islam, Saeed, 2020. "Resonant optical solitons of nonlinear Schrödinger equation with dual power law nonlinearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).

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