Acta Physica Sinica, Vol. 69, Issue 1, 010203-1 (2020)
The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability
Liu Ping1,*, Xu Heng-Rui2, and Yang Jian-Rong3
- 1School of Electronic and Information Engineering, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China
- 2School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
- 3School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China
The Boussinesq equation is a very important equation in fluid mechanics and some other disciplines. A Lax pair of the Boussinesq equation is proposed. With the help of the truncated Painlevé expansion, auto-B?cklund transformation of the Boussinesq equation and B?cklund transformation between the Boussinesq equation and the Schwarzian Boussinesq equation are demonstrated. Nonlocal symmetries of the Boussinesq equation are discussed. One-parameter subgroup invariant solutions and one-parameter group transformations are obtained. The consistent Riccati expansion solvability of the Boussinesq equation is proved and some interaction structures between soliton-cnoidal waves are obtained by consistent Riccati expansion.
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