Journal of Experimental and Theoretical Physics

, Volume 93, Issue 6, pp 1307–1313 | Cite as

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

  • Yu. N. Ovchinnikov
  • V. L. Vereshchagin
Nonlinear Physics


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, C1). At large values of C1 (C1→∞), 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 C1.


Spectroscopy State Physics Field Theory Elementary Particle Quantum Field Theory 
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  1. 1.
    V. E. Zakharov, Zh. Éksp. Teor. Fiz. 62, 1746 (1972) [Sov. Phys. JETP 35, 908 (1972)].Google Scholar
  2. 2.
    V. E. Zakharov and V. S. Sinakh, Zh. Éksp. Teor. Fiz. 68, 940 (1975) [Sov. Phys. JETP 41, 465 (1975)].Google Scholar
  3. 3.
    V. E. Zakharov and L. N. Shchur, Zh. Éksp. Teor. Fiz. 81, 2019 (1981) [Sov. Phys. JETP 54, 1064 (1981)].Google Scholar
  4. 4.
    V. E. Zakharov and E. A. Kuznetsov, Zh. Éksp. Teor. Fiz. 91, 1310 (1986) [Sov. Phys. JETP 64, 773 (1986)].ADSGoogle Scholar
  5. 5.
    Yu. N. Ovchinnikov, Pis’ma Zh. Éksp. Teor. Fiz. 69, 387 (1999) [JETP Lett. 69, 418 (1999)].Google Scholar
  6. 6.
    Yu. N. Ovchinnikov and I. M. Sigal, Zh. Éksp. Teor. Fiz. 116, 67 (1999) [JETP 89, 35 (1999)].MathSciNetGoogle Scholar
  7. 7.
    C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer-Verlag, New York, 1999).Google Scholar
  8. 8.
    Yu. N. Ovchinnikov and V. L. Vereshchagin, Pis’ma Zh. Éksp. Teor. Fiz. 74, 76 (2001) [JETP Lett. 74, 72 (2001)].Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2001

Authors and Affiliations

  • Yu. N. Ovchinnikov
    • 1
    • 2
  • V. L. Vereshchagin
    • 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.Institute of Mathematics and Computing CenterUral Division Russian Academy of SciencesYekaterinburgRussia

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