Lie group analysis : Classical Heritage

TL;DRAbstract

Classical works in Lie group analysis, e.g. important papers of S.Lie and A.V.Bäcklund are written in old German and somewhat old fashioned mathematical language. The present volume comprises translation into English of fundamental papers of S. Lie, A.V.Bäcklund and L.V. Ovsyannikov. I have selected here some of my favorite papers containing profound results significant for modern group analysis. The first paper imparts not only Lie's interesting view on the development of the general theory of differential equations but also contains Lie's theory of group invariant solutions. His second paper is dedicated to group classification of second-order linear partial differential equations in two variables and can serve as a concise practical guide to the group analysis of partial differential equations even today. The translation of Bäcklund's fundamental paper on non-existence of finite-order tangent transformations higher than first-order contains roots of the modern theory of Lie-Bäcklund

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