Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalised variable coefficient shallow water wave equation

2019/01/22 by Xiangpeng Xin, Xin, Xiangpeng, Linlin Zhang +5
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1901.07307

arxiv created 2019/01/22 · arxiv updated 2019/01/23

Abstract

In this paper, using the standard truncated Painleve analysis, the Schwartzian equation of (2+1)-dimensional generalised 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 on illustrate dynamic behavior of the generalised variable coefficient SWW equation.

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