Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation

Abstract

In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. By calculating the vector field of the potential function, the interaction between lump waves and solitary waves is studied in detail. Lumps can emerge from the solitary wave and are semi-localized in time. The analytical solutions may enrich our understanding of the nature of shallow-water waves.

Keywords

• lump waves
• lump-solitary interaction
• (2+1)-dimensional shallow-water wave
• Hirota’s bilinear method