E-Book, Englisch, Band 299, 258 Seiten, eBook
Gaeta Nonlinear Symmetries and Nonlinear Equations
1994
ISBN: 978-94-011-1018-1
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 299, 258 Seiten, eBook
Reihe: Mathematics and Its Applications
ISBN: 978-94-011-1018-1
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark
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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Weitere Infos & Material
List of abbreviations. Foreword. Introduction. I: Geometric setting. a) Equations and functions as geometrical objects. b) Symmetry. II: Symmetries and their use. III: Examples. IV: Evolution equations. a) Evolution equations -- general features. b) Dynamical systems (ODEs). c) Periodic solutions. d) Evolution PDEs. V: Variational problems. VI: Bifurcation problems. VII: Gauge theories. VIII: Reduction and equivariant branching lemma. IX: Further developments. X: Equations of physics. References and bibliography. Subject Index.
