Lie’s Infinitesimal Continous Similarity Transformtion Method of Finding Particulr Solutions of Partial Differential Equations and It’s Limitations

Abstract

Lie’s continuous infinitesimal similarity transformation method of finding exact solutions of nonlinear partial differential equations widely using in Theoretical Physics and Fluid Dynamics .The limitations of this method is, restricted to a class of particular solutions and there may exist other particular solutions outside this class . So, in most cases Lie’s continuous infinitesimal similarity transformation method fails to obtain general solutions of nonlinear partial differential equations.