Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

doi:10.1088/1674-1056/acf11c

中国物理B ›› 2023, Vol. 32 ›› Issue (11): 110206-110206.doi: 10.1088/1674-1056/acf11c

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Xi-Zhong Liu(刘希忠), Jie-Tong Li(李界通), and Jun Yu(俞军)^†

Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China

收稿日期:2023-05-17 修回日期:2023-08-11 接受日期:2023-08-17 出版日期:2023-10-16 发布日期:2023-11-03
通讯作者: Jun Yu E-mail:junyu@usx.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148).

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Xi-Zhong Liu(刘希忠), Jie-Tong Li(李界通), and Jun Yu(俞军)^†

Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China

Received:2023-05-17 Revised:2023-08-11 Accepted:2023-08-17 Online:2023-10-16 Published:2023-11-03
Contact: Jun Yu E-mail:junyu@usx.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148).

摘要/Abstract

摘要： 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.

关键词: (3+1)-dimensional shallow water wave equation, residual symmetry, consistent Riccati expansion

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.

Key words: (3+1)-dimensional shallow water wave equation, residual symmetry, consistent Riccati expansion

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 05.45.Yv (Solitons) 47.35.Fg (Solitary waves)

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[J]. 中国物理B, 2023, 32(11): 110206-110206.

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Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

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