The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability-Reference-Cited by-同舟云学术

The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability

Published:2020 Issue:1 Volume:69 Page:010203
ISSN:1000-3290
Container-title:Acta Physica Sinica
language:
Short-container-title:Acta Phys. Sin.

Author:

Liu Ping,Xu Heng-Rui,Yang Jian-Rong, , ,

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-Bäcklund transformation of the Boussinesq equation and Bäcklund 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.

Publisher

Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences

Subject

General Physics and Astronomy

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