The method of symmetry reduction is used to solve Grassmann-valued differential equations. The (Nϭ2) supersymmetric Korteweg-de Vries equation is considered. It admits a Lie superalgebra of symmetries of dimension 5. A two-dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation. We are then able to give different types of exact solutions, in particular soliton solutions.
Working in a superspace, we compute the Lie-point symmetries for the supersymmetric two bosons equations. Computer algebra has helped us to skip the tedious calculations. Translational symmetry supergroups are used to reduce the supersymmetric two bosons equations to an ordinary differential supersystem which involves two even and two odd dependent variables. Some explicit solutions are presented.PACS numbers: 02.20.Sv, 02.30.Jr, 11.30.Pb.
RésuméDans le superespace, nous calculons le groupe de Lie des symétries pour leséquationsà deux bosons supersymétriques. Le programme GLieécrit dans le langage MAPLE nous permet d'écrire facilement les superéquations déterminantes qui conduisent aux géné-rateurs de la superalgèbre correspondante. On impose l'invariance par translations des solutions pour réduire le supersytémeà un supersystème contenant une seule variable indépendante. Ce dernier se décompose en quatreéquations contenant deux variables dé-pendantes paires et deux impaires. Finalement, on présente quelques solutions explicites.
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