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Multiparameter family of collapsing solutions to the critical nonlinear Schrödinger equation in dimension D=2

  • Yu. N. Ovchinnikov
  • I. M. Sigal
Nonlinear Physics

Abstract

We consider the critical nonlinear Schrödinger equation in dimension D=2 and obtain a system consisting of three equations describing the collapse of solutions. The system admits a five-parameter family of solutions. Almost everywhere, except for an exponentially narrow region near the collapse point, the tunneling processes are negligible. The relation between initial data and the condition of occurrence of the collapse is investigated. The separatrix, which divides the collapse domain and expansion regions having no singularities in a finite time interval, is found.

Keywords

Spectroscopy State Physics Field Theory Elementary Particle Initial Data 
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Copyright information

© MAIK "Nauka/Interperiodica" 2003

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 SciencesChernogolovka, Moscow oblastRussia
  3. 3.Department of MathematicsUniversity of TorontoOntarioCanada

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