Nonlocal Symmetry of the Lax Equation Related to Riccati-Type Pseudopotential

doi:10.1088/0256-307X/29/12/120503

Chin. Phys. Lett.

2012, Vol. 29

Issue (12): 120503 DOI: 10.1088/0256-307X/29/12/120503

GENERAL

Nonlocal Symmetry of the Lax Equation Related to Riccati-Type Pseudopotential

WANG Yun-Hu, CHEN Yong^**, XIN Xiang-Peng

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062

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WANG Yun-Hu, CHEN Yong, XIN Xiang-Peng 2012 Chin. Phys. Lett. 29 120503

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Abstract We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity. A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones. It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential. By introducing suitable and simple auxiliary dependent variables, the nonlocal symmetry is localized and used to generate new solutions from trivial solutions. Meanwhile, this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.

Received: 04 September 2012 Published: 04 March 2013

PACS:	05.45.Yv	(Solitons)
	03.65.Ge	(Solutions of wave equations: bound states)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/29/12/120503 OR https://cpl.iphy.ac.cn/Y2012/V29/I12/120503

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