Similarity analysis of differential equations by Lie group

Abstract

Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analyses in a broader sense--namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations--is given with new and very general methods evolved for deriving the possible groups of transformations.