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Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system

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  • Gao, Xin-Yi
  • Guo, Yong-Jiang
  • Shan, Wen-Rui

Abstract

Oceanic water waves are actively studied. Hereby, taking into account the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of finite depth, we investigate a generalized (2+1)-dimensional dispersive long-wave system. With symbolic computation while with respect to the horizontal velocity and wave elevation above the undisturbed water surface, we work out two non-auto-Bäcklund transformations and two auto-Bäcklund transformations with solitons. All of our results are dependent on the constant coefficients in the original system.

Suggested Citation

  • Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2020. "Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303490
    DOI: 10.1016/j.chaos.2020.109950
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    Cited by:

    1. Bakıcıerler, Gizel & Alfaqeih, Suliman & Mısırlı, Emine, 2021. "Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Xie, Yingying & Li, Lingfei, 2022. "Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 19-31.
    3. Shahu, Chiranjeev K. & Dwivedi, Sharad & Dubey, Shruti, 2022. "Curved domain walls in the ferromagnetic nanostructures with Rashba and nonlinear dissipative effects," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Chen, Su-Su & Tian, Bo & Qu, Qi-Xing & Li, He & Sun, Yan & Du, Xia-Xia, 2021. "Alfvén solitons and generalized Darboux transformation for a variable-coefficient derivative nonlinear Schrödinger equation in an inhomogeneous plasma," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2022. "Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Wang, Pan & Ma, Tian-Ping & Qi, Feng-Hua, 2021. "Analytical solutions for the coupled Hirota equations in the firebringent fiber," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    7. Yang, Dan-Yu & Tian, Bo & Qu, Qi-Xing & Zhang, Chen-Rong & Chen, Su-Su & Wei, Cheng-Cheng, 2021. "Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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