The purpose of this paper is to discuss the homoclinic breathe-wave solutions and the singular periodic solutions for (2 + 1)-dimensional generalized shallow water wave (GSWW) equation.
The Hirota bilinear method, the Lie symmetry method and the non-Lie symmetry method are applied to the (2 + 1)D GSWW equation.
A reduced (1 + 1)D potential KdV equation can be derived, and its soliton solutions are also presented.
As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.
These results are very useful for investigating some localized geometry structures of dynamical behaviors and enriching dynamical features of solutions for the higher dimensional systems.
This work was supported by Longshan Scholar Talent Research Supporting Program of SWUST (17LZXY04, 17LZXJ05).
Xiaorong, K. and Daquan, X. (2019), "Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 3, pp. 1000-1009. https://doi.org/10.1108/HFF-08-2018-0436Download as .RIS
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