Abstract
Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of \((3\,{+}\,1)\)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, 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.
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Acknowledgements
The authors acknowledge National Natural Science Foundation of China (Grant Nos 11571049 and 61370195) and Science and Technology project of Jiangxi Provincial Health and Family Planning Commission (20175537).
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Li, YZ., Liu, JG. Multiple periodic-soliton solutions of the \((3+1)\)-dimensional generalised shallow water equation. Pramana - J Phys 90, 71 (2018). https://doi.org/10.1007/s12043-018-1568-3
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DOI: https://doi.org/10.1007/s12043-018-1568-3