Lie group analysis: Classical Heritage
|Author(s):||Nail H. Ibragimov|
|Title:||Lie group analysis: Classical Heritage|
|Translated title:||Liegruppanalys: Klassiskt arv|
|Organization:||Blekinge Institute of Technology|
|Department:||School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
|Abstract:||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 transformation groups.
Finally, Ovsyannikov's paper contains an essential development of the group classification of hyperbolic equations given in Lie's second paper. Moreover, it contains two proper invariants for hyperbolic equations discovered by Ovsyannikov.
|Keywords:||Lie group analysis, Differential Equations, S.Lie|
|Note:||The monograph is published by ALGA Publications and is available at: http://www.bth.se/alga/|