Multiple periodic-soliton solutions of the (3 + 1)-dimensional generalised shallow water equation

摘要

Based on the extended variable-coefficient homogeneous balance method and two newans?¤tz functions, we construct auto-B?¤cklund transformation and multiple periodic-soliton solutions of (3+1)-dimensional generalised shallowwater equations.Completely newperiodic-soliton solutions including periodic cross-kinkwave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.