Abstract Two (3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion (CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new Bäcklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148).
Corresponding Authors:
Jun Yu
E-mail: junyu@usx.edu.cn
Cite this article:
Xi-Zhong Liu(刘希忠), Jie-Tong Li(李界通), and Jun Yu(俞军) Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations 2023 Chin. Phys. B 32 110206
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