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Genetic Codes of Lie Algebras and Nonlinear Evolution Equations

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Nonlinear Evolution Equations and Dynamical Systems

Part of the book series: Research Reports in Physics ((RESREPORTS))

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Abstract

A set of generators and determining relations for a free Lie algebra will be called its ”genetic code” in accordance with the terminology from discrete group theory [1]. Computer analysis [2] of such genetic codes is very important, in particular, for Walhquist- Estabrook (W-E) method [3] in theory of nonlinear partial differential equations (NPDEs). In the present paper we propose the method which is reverse to W-E method, that is to restore NPDE given by a genetic code. It should be noted that different NPDEs may have the same genetic code.

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References

  1. Coxeter H. S. M., Moser W. O. J. Generators and Relations for Discrete Groups. Third Edition. Springer-Verlag, Berlin, 1972.

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  2. Akselrod I. R., Gerdt V. P., Kovtim V. E., Robuk V. N. Construction of a Lie Algebra by a Subset of Generators and Commutation Relations. Preprint JINR E5-90-508, Dubna, 1990.

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  3. Walhquist H. D., Estabrook F. B. Prolongation Structures of Nonlinear Evolution Equations. J. Math. Phys. 16, 1, 1–7, 1975.

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  4. Marchenko V. A. Nonlinear Equations and Operator Algebras. Kiev, Naukova Dumka, 1986 (in Russian).0

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Author information

Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Head P.O. Box 79, SU-101000, Moscow, USSR

    V. P. Gerdt

  2. Kharkov State University, Kharkov, USSR

    V. E. Kovtun

  3. Institute for Low Temperature Physics and Technology, 47 Lenin Avenue, SU-310164, Kharkov, USSR

    V. N. Robuk

Authors
  1. V. P. Gerdt
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  2. V. E. Kovtun
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  3. V. N. Robuk
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, P.O. Box 79, Head Post Office, SU-101100, Moscow, USSR

    Vladimir G. Makhankov  & Oktay K. Pashaev  & 

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© 1991 Springer-Verlag Berlin Heidelberg

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Gerdt, V.P., Kovtun, V.E., Robuk, V.N. (1991). Genetic Codes of Lie Algebras and Nonlinear Evolution Equations. In: Makhankov, V.G., Pashaev, O.K. (eds) Nonlinear Evolution Equations and Dynamical Systems. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76172-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-76172-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53294-1

  • Online ISBN: 978-3-642-76172-0

  • eBook Packages: Springer Book Archive

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