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

Abstract

Abstract 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.