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

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 lin...

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Bibliographic Details
Published inChinese physics letters Vol. 29; no. 12; pp. 120503 - 1-120503-3
Main Authors Wang, Yun-Hu, Chen, Yong, Xin, Xiang-Peng
Format Journal Article
LanguageEnglish
Published 01.12.2012
Subjects
Dependent variables
Differential equations
Exact solutions
Mathematical analysis
Mathematical models
Pseudopotentials
Shallow water
Symmetry
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Summary: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.
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ISSN:0256-307X
1741-3540
DOI:10.1088/0256-307X/29/12/120503