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Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system

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  • Liu, Yaqing
  • Peng, Linyu

Abstract

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries (KdV) system by its analytic solutions. Its N-soliton solutions are obtained via Hirota’s bilinear method, and in particular, the hybrid solutions of lump, breather and line solitons are derived by the long wave limit method. In addition to soliton solutions, similarity reduction, including similarity solutions (also known as group-invariant solutions) and novel non-autonomous rational third-order Painlevé equations, is achieved through symmetry analysis. The analytic results, together with illustrative wave interactions, show interesting physical features, that may shed some light on the study of other variable-coefficient nonlinear systems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003314
    DOI: 10.1016/j.chaos.2023.113430
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    References listed on IDEAS

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    1. Kumar, Raj & Kumar, Avneesh, 2022. "Dynamical behavior of similarity solutions of CKOEs with conservation law," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Ma, Yu-Lan & Li, Bang-Qing, 2022. "Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
    4. Li, Bang-Qing & Ma, Yu-Lan, 2022. "Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing electromagnetic systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. 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.
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