Residual Symmetry Analysis for Novel Localized Excitations of a (2+1)-Dimensional General Korteweg-de Vries System

The nonlocal residual symmetry of a (2+1)-dimensional general Korteweg-de Vries (GKdV) system is derived by the truncated Painlevé analysis. The nonlocal residual symmetry is then localized to a Lie point symmetry by introducing auxiliary-dependent variables. By using Lie’s first theorem, the finite...

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Published inZeitschrift für Naturforschung. A, A journal of physical sciences Vol. 72; no. 9; pp. 795 - 804
Main Authors Zhu, Quanyong, Fei, Jinxi, Ma, Zhengyi
Format Journal Article
LanguageEnglish
Published De Gruyter 01.09.2017
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Summary:The nonlocal residual symmetry of a (2+1)-dimensional general Korteweg-de Vries (GKdV) system is derived by the truncated Painlevé analysis. The nonlocal residual symmetry is then localized to a Lie point symmetry by introducing auxiliary-dependent variables. By using Lie’s first theorem, the finite transformation is obtained for the localized residual symmetry. Furthermore, multiple Bäcklund transformations are also obtained from the Lie point symmetry approach via the localization of the linear superpositions of multiple residual symmetries. As a result, various localized structures, such as dromion lattice, multiple-soliton solutions, and interaction solutions can be obtained through it; and these localized structures are illustrated by graphs.
ISSN:0932-0784
1865-7109
DOI:10.1515/zna-2017-0124