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.

Fund: 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).

Corresponding Authors:
Jun Yu,E-mail:junyu@usx.edu.cn
E-mail: junyu@usx.edu.cn

About author: 2021-12-16

Cite this article:

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

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