TY  - JOUR
AB  - Purpose 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.Design/methodology/approach The Hirota bilinear method, the Lie symmetry method and the non-Lie symmetry method are applied to the (2 + 1)D GSWW equation.Findings A reduced (1 + 1)D potential KdV equation can be derived, and its soliton solutions are also presented.Research limitations/implications As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.Originality/value 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.
VL  - 29
IS  - 3
SN  - 0961-5539
DO  - 10.1108/HFF-08-2018-0436
UR  - https://doi.org/10.1108/HFF-08-2018-0436
AU  - Xiaorong Kang
AU  - Daquan Xian
PY  - 2018
Y1  - 2018/01/01
TI  - Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation
T2  - International Journal of Numerical Methods for Heat & Fluid Flow
PB  - Emerald Publishing Limited
SP  - 1000
EP  - 1009
Y2  - 2024/05/04
ER  -