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  • Received: Sep. 2, 2019

    Accepted: --

    Posted: Nov. 4, 2020

    Published Online: Nov. 4, 2020

    The Author Email: Xu Heng-Rui (liuping49@126.com)

    DOI: 10.7498/aps.69.20191316

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    Ping Liu, Heng-Rui Xu, Jian-Rong Yang. The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability[J]. Acta Physica Sinica, 2020, 69(1): 010203-1

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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

Author Affiliations

  • 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

Abstract

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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