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The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

  • Nonlinear Physics
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Abstract

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton.

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Authors and Affiliations

  1. Verkin Physicotechnical Institute of Low Temperatures, National Academy of Sciences of Ukraine, Kharkov, 61164, Ukraine

    A. M. Kosevich

  2. Max-Plank-Institut für Physik Komplexer Systeme, D01187, Dresden, Germany

    A. M. Kosevich

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  1. A. M. Kosevich
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 119, No. 5, 2001, pp. 995–1000.

Original Russian Text Copyright © 2001 by Kosevich.

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Kosevich, A.M. The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation. J. Exp. Theor. Phys. 92, 866–870 (2001). https://doi.org/10.1134/1.1378180

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  • DOI: https://doi.org/10.1134/1.1378180

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