A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

doi:10.1088/1674-1056/ac43a7

中国物理B ›› 2022, Vol. 31 ›› Issue (5): 50201-050201.doi: 10.1088/1674-1056/ac43a7

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A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

Xi-zhong Liu(刘希忠) and Jun Yu(俞军)^†

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

收稿日期:2021-10-24 修回日期:2021-12-01 出版日期:2022-05-14 发布日期:2022-04-29
通讯作者: Jun Yu,E-mail:junyu@usx.edu.cn 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) and the Natural Science Foundation of Zhejiang Province of China (Grant No.LY18A050001).

A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

Xi-zhong Liu(刘希忠) and Jun Yu(俞军)^†

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

Received:2021-10-24 Revised:2021-12-01 Online:2022-05-14 Published:2022-04-29
Contact: Jun Yu,E-mail:junyu@usx.edu.cn E-mail:junyu@usx.edu.cn
About author:2021-12-16
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.11975156 and 12175148) and the Natural Science Foundation of Zhejiang Province of China (Grant No.LY18A050001).

摘要/Abstract

摘要： A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.

关键词: nonlocal Boussinesq equation, N-soliton solution, periodic waves, symmetry reduction solutions

Abstract: A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.

Key words: nonlocal Boussinesq equation, N-soliton solution, periodic waves, symmetry reduction solutions

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) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201.

Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. Chin. Phys. B, 2022, 31(5): 50201-050201.

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A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

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