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Properties of weakly collapsing solutions to the nonlinear Schrödinger equation

  • Yu. N. Ovchinnikov
Nonlinear Physics

Abstract

It is shown that one of the conditions for a weakly collapsing solution with zero energy produces an infinite number of functionals I N identically vanishing on the regular solutions to the corresponding differential equation. On the parameter plane {A, C1}, there are at least two singular lines. Along one of these lines (A/C1=1/6), are located weakly collapsing solutions with zero energy. It is assumed that, along the second line (A/C1c), another family of weakly collapsing solutions with zero energy is located. In the domain of large values of the parameters C1, α=A/C1, there exists a domain of an intermediate asymptotic form, where the amplitude of oscillations of the function U grows in a large domain relative to the ξ coordinate.

Keywords

Spectroscopy Differential Equation State Physics Field Theory Elementary Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • Yu. N. Ovchinnikov
    • 1
    • 2
  1. 1.Max-Planck Institute for Physics of Complex SystemsDresdenGermany
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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