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Symmetries and conservation laws of dynamical systems

  • Non-Linear Systems
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  • First Online:
Book cover Twistor Geometry and Non-Linear Systems

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

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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.

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References

  1. Gardner C.S., Greene J.M., Kruskal M.D., Miura R.M., Method for solving the KdV equation, Phys.Rev.Lett.,19, No. 19 (1967), 1095–1087.

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  4. V.K. Mel’nikov, On the equations generating operator relations, (in russian), Mat. Sb. 108, No.3, (1979), 378–392.

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  5. V.K. Mel’nikov, On conservation laws for one class systems of non-linear evolution equations, (in russian), Preprint Joint Institute of Nuclear Research, R5-12060,Dubna, 1978.

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  6. V.K. Mel’nikov, Symmetries and conservation laws, (in russian), Preprint Joint Institute of Nuclear Research, R2-12304, Dubna, 1979.

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Authors and Affiliations

  1. Joint Institute of Nuclear Research, 141980, Dubna, Russia

    V. K. Mel’nikov

Authors
  1. V. K. Mel’nikov
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Heinz-Dietrich Doebner Tchavdar D. Palev

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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

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