Lie symmetries and reductions via invariant solutions of general short pulse equation

Around 1880, Lie introduced an idea of invariance the partial differential equation (PDE) under one-parameter group transformation to find invariant, similarity, or auto-model solutions. symmetry analysis (LSA) provides us algorithm search for point symmetries solving related linear systems infinitesimal generators. Actually, lead family solutions from a known solution. LSA is program that exact non-linear equations (DEs) in analogy designed by Galois algebraic polynomial equations. In this paper, we have carried out computing similarity (symmetries) short pulse (SPE) cases when h ( u ) = e , k xx h(u)=eun and . addition, optimal system one-dimensional sub-algebra has been set up. The reductions invariant generalized SPE are calculated corresponding as well. Reductions reduce PDE PDEs into reduced ordered ODE PDEs. This helps solve these form. Graphical behavior transformed points 1-parameter solution functions drawn.