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Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

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  • N. V. Ustinov

Abstract

The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • N. V. Ustinov, 2007. "Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(3), pages 311-317, August.
    • Handle: RePEc:spr:eurphb:v:58:y:2007:i:3:p:311-317
    DOI: 10.1140/epjb/e2007-00224-2
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