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New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method

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  • Chen, Yong
  • Yan, Zhenya

Abstract

In this paper, (2+1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2+1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions.

Suggested Citation

  • Chen, Yong & Yan, Zhenya, 2005. "New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 399-406.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:399-406
    DOI: 10.1016/j.chaos.2005.01.004
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    Cited by:

    1. Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal Gardner equation," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.
    3. Chaudry Masood Khalique & Oke Davies Adeyemo, 2020. "Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    4. Aly R. Seadawy & Hanadi Zahed & Mujahid Iqbal, 2022. "Solitary Wave Solutions for the Higher Dimensional Jimo-Miwa Dynamical Equation via New Mathematical Techniques," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    5. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.

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