Lie symmetry analysis for generalized short pulse equation

Abstract

Lie symmetry analysis (LSA) is one of the most common, effective, and estimation-free methods to find the symmetries and solutions of the differential equations (DEs) by following an algorithm. This analysis leads to reduce the order of partial differential equations (PDEs). Many physical problems are converted into non-linear DEs and these DEs or system of DEs are then solved with several methods such as similarity methods, Lie Bäcklund transformation, and Lie group of transformations. LSA is suitable for providing the conservation laws corresponding to Lie point symmetries or Lie Bäcklund symmetries. Short pulse equation (SPE) is a non-linear PDE, used in optical fibers, computer graphics, and physical systems and has been generalized in many directions. We will find the symmetries and a class of solutions depending on one-parameter (ε) obtained from Lie symmetry groups. Then we will construct the optimal system for the Lie algebra and invariant solutions (called similarity solutions) from Lie subalgebras of generalized SPE.

Keywords

• short pulse equation
• lie symmetry
• invariant solutions
• optimal system
• reductions