Properties of weakly collapsing solutions to the nonlinear Schrödinger equation
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, C_{1}}, there are at least two singular lines. Along one of these lines (A/C_{1}=1/6), are located weakly collapsing solutions with zero energy. It is assumed that, along the second line (A/C_{1}=α_{c}), another family of weakly collapsing solutions with zero energy is located. In the domain of large values of the parameters C_{1}, α=A/C_{1}, 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.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 May 2003
 DOI:
 10.1134/1.1581953
 Bibcode:
 2003JETP...96..975O
 Keywords:

 Spectroscopy;
 Differential Equation;
 State Physics;
 Field Theory;
 Elementary Particle