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Local Nonintegrability of Long—Short Wave Interaction Equations

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Symmetries of Partial Differential Equations

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Abstract

The algebra of higher symmetries and the space of conservation laws for Zakharov’s nonlinear equations of the interaction between long and short waves are completely described. The scheme of computations due to Vinogradov is used. As a result, the local nonintegrability of these equations is proved.

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References

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Author information

Authors and Affiliations

  1. Organization of Production, and Economic Information Research Institute (VNIIEGASPROM), All-Union Gas Industry Economics, Kazansky Lane 7/19, 117049, Moscow, USSR

    A. M. Verbovetsky

Authors
  1. A. M. Verbovetsky
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Editor information

Editors and Affiliations

  1. Moscow State University, USSR

    A. M. Vinogradov

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© 1989 Kluwer Academic Publishers

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Verbovetsky, A.M. (1989). Local Nonintegrability of Long—Short Wave Interaction Equations. In: Vinogradov, A.M. (eds) Symmetries of Partial Differential Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1948-8_5

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  • DOI: https://doi.org/10.1007/978-94-009-1948-8_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7370-7

  • Online ISBN: 978-94-009-1948-8

  • eBook Packages: Springer Book Archive

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