2011•Journal of Natural Science of Heilongjiang UniversityRequires access

The admitted symmetries of the generalized Hirota-Satsuma coupled KdV equation and applications

Wang Shan-wei

Abstract

The generalized Hirota-Satsuma coupled KdV equation is taken as the research object,the symmetry group theorem is firstly considered by means of the classical Lie point symmetry method.Then,the new explicit and exact solutions under the groups are obtained.Secondly,all the admitted four-order symmetries are studied.Finally,the equation's five conservation laws in cases are also given,which are regarded as the symmetry's important application in physics.

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Key concepts: Korteweg–de Vries equation, Homogeneous space, Symmetry (geometry), Mathematics, Mathematical physics, Conservation law, Point (geometry), Order (exchange)