Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation

Abstract

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.