Acta Physica Sinica, Volume. 69, Issue 1, 010203-1(2020)
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.
Get Citation
Copy Citation Text
Ping Liu, Heng-Rui Xu, Jian-Rong Yang.
Received: Sep. 2, 2019
Accepted: --
Published Online: Nov. 4, 2020
The Author Email: