Nonlinear Symmetries and Nonlinear Equations

Nonlinear Symmetries and Nonlinear Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 275
Release :
ISBN-10 : 9789401110181
ISBN-13 : 9401110182
Rating : 4/5 (182 Downloads)

Book Synopsis Nonlinear Symmetries and Nonlinear Equations by : G. Gaeta

Download or read book Nonlinear Symmetries and Nonlinear Equations written by G. Gaeta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.


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This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear