Nonlinear Symmetries and Nonlinear Equations

Released on by G. Gaeta
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  • Nonlinear Symmetries and Nonlinear Equations Book Detail

  • Author : G. Gaeta
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 275
  • ISBN 13 : 9401110182
  • File Size : 21,21 MB
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Nonlinear Symmetries and Nonlinear Equations by G. Gaeta PDF Summary

Book Description: 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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