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Symmetries and conservation laws of dynamical systems

Non-Linear Systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 970)

Abstract

We have considered all nonlinear evolution equations generated by the operator relation

where L is the differential operator of the form

and A, B are rationally dependent on parameter η differential operators. We have found the infinite dimensional group of symmetries of equations thus obtained. Several infinite series of conservation laws are also found which are satisfied by the solutions of these equations.

Keywords

  • Diagonal Element
  • Recurrence Relation
  • Soliton Solution
  • Formal Series
  • Nonlinear Evolution Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1982 Spring-Verlag

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Mel’nikov, V.K. (1982). Symmetries and conservation laws of dynamical systems. In: Doebner, HD., Palev, T.D. (eds) Twistor Geometry and Non-Linear Systems. Lecture Notes in Mathematics, vol 970. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066029

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  • DOI: https://doi.org/10.1007/BFb0066029

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11972-2

  • Online ISBN: 978-3-540-39418-1

  • eBook Packages: Springer Book Archive