Based on the extended variable-coefficient homogeneous balance method and two newansätz functions, we construct auto-Bäcklund 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.
Volume 97, 2023
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