Gaeta G. Nonlinear Symmetries and Nonlinear Equations 1994

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The study of (nonlinear) differential 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.
Front Matter
Geometric setting
Symmetries and their use
Examples
Evolution equations
Variational problems
Bifurcation problems
Gauge theories
Reduction and equivariant branching lemma
Further Developements
Equations of Physics
Back Matter