Explicit solutions from residual symmetry of the Boussinesq equation

doi:10.1088/1674-1056/24/3/030202

Abstract The Bäcklund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the Boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained: a new type of Bäcklund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.

Keywords: Boussinesq equation localization procedure residual symmetry symmetry reduction solution

Received: 23 August 2014
Revised: 12 October 2014
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)
	47.35.Fg	(Solitary waves)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11405110, 11275129, and 11305106) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).

Corresponding Authors: Liu Xi-Zhong
E-mail: liuxizhong123@163.com

Cite this article:

Liu Xi-Zhong (刘希忠), Yu Jun (俞军), Ren Bo (任博) Explicit solutions from residual symmetry of the Boussinesq equation 2015 Chin. Phys. B 24 030202

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