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Nonlocal symmetries and exact solutions of the \((2+1)\)-dimensional generalized variable coefficient shallow water wave equation. (English) Zbl 1412.35020

Summary: In this paper, using the standard truncated Painlevé analysis, the Schwartzian equation of \((2+1)\)-dimensional generalized variable coefficient shallow water wave (SWW) equation is obtained. With the help of Lax pairs, nonlocal symmetries of the SWW equation are constructed which be localized by a complicated calculation process. Furthermore, using the Lie point symmetries of the closed system and Schwartzian equation, some exact interaction solutions are obtained, such as soliton-cnoidal wave solutions. Corresponding 2D and 3D figures are placed to illustrate dynamic behavior of the generalized variable coefficient SWW equation.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35Q35 PDEs in connection with fluid mechanics

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References:

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