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The properties of weakly collapsing solutions to the nonlinear Schrödinger equation at large values of the free parameters

  • Nonlinear Physics
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Abstract

It is shown that there exists an infinite set of weakly collapsing solutions with zero energy. Zero energy solutions are distributed along two lines in the space of parameters (A, C 1). At large values of C 1 (C 1→∞), the distance between the nearest points on every line tends to a finite limit. Along each of the lines, the amplitude of the oscillating terms is exponentially small with respect to the parameter C 1.

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Authors and Affiliations

  1. Max Planck Institute for Physics of Complex Systems, Dresden, D-01187, Germany

    Yu. N. Ovchinnikov

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    Yu. N. Ovchinnikov

  3. Institute of Mathematics and Computing Center, Ural Division Russian Academy of Sciences, Yekaterinburg, 620219, Russia

    V. L. Vereshchagin

Authors
  1. Yu. N. Ovchinnikov
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  2. V. L. Vereshchagin
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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. 120, No. 6, 2001, pp. 1509–1516.

Original Russian Text Copyright © 2001 by Ovchinnikov, Vereshchagin.

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Ovchinnikov, Y.N., Vereshchagin, V.L. The properties of weakly collapsing solutions to the nonlinear Schrödinger equation at large values of the free parameters. J. Exp. Theor. Phys. 93, 1307–1313 (2001). https://doi.org/10.1134/1.1435754

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  • DOI: https://doi.org/10.1134/1.1435754

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