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Collapse in the nonlinear Schrödinger equation of critical dimension {σ=1, D=2}

  • Yu. N. Ovchinnikov
  • I. M. Sigal
Methods of Theoretical Physics

Abstract

Collapsing solutions to the nonlinear Schrödinger equation of critical dimension {σ=1, D=2} are analyzed in the adiabatic approximation. A three-parameter set of solutions is obtained for the scale factor λ(t). It is shown that the Talanov solution lies on the separatrix between the regions of collapse and convenient expansion. A comparison with numerical solutions indicates that weakly collapsing solutions provide a good initial approximation to the collapse problem.

PACS numbers

02.30.Jr 03.65.Ge 

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Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • Yu. N. Ovchinnikov
    • 1
    • 2
  • I. M. Sigal
    • 3
  1. 1.Max-Planck Institute for Physics of Complex SystemsDresdenGermany
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada

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