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Nonlinear Symmetries and Nonlinear Equations

Nonlinear Symmetries and Nonlinear Equations

Paperback

Series: Mathematics and Its Applications, Book 299

General GardeningGeneral MathematicsPhysics

ISBN10: 9401044430
ISBN13: 9789401044431
Publisher: Springer Nature
Published: Oct 14 2012
Pages: 258
Weight: 0.89
Height: 0.60 Width: 6.14 Depth: 9.21
Language: English
The study of (nonlinear) difterential 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 difterent 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 difterential 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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