Properties of weakly collapsing solutions to the nonlinear Schrödinger equation

  • Yu. N. Ovchinnikov
Nonlinear Physics


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.


Spectroscopy Differential Equation State Physics Field Theory Elementary Particle 
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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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