Nonlocal symmetries and explicit solutions for the Gardner equation

From the known Lax pair of the Gardner equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the Gardner equation with nonlocal symmetries by introducing suitable auxiliary dependent variables. Based on the prolonged system, the explicit analytic solut...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 314; pp. 293 - 298
Main Authors Fei, Jinxi, Cao, Weiping, Ma, Zhengyi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2017
Subjects
Explicit solution
Gardner equation
Lax pair
Nonlocal symmetry
Nonlocal symmetry
Gardner equation
Lax pair
Explicit solution
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Summary:From the known Lax pair of the Gardner equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the Gardner equation with nonlocal symmetries by introducing suitable auxiliary dependent variables. Based on the prolonged system, the explicit analytic solutions related to the Jacobi elliptic functions are derived. Figures illustrate the interaction between the cnoidal waves and a kink wave.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.07.002