Properties of weak-collapsing solutions of nonlinear Schroedinger equation

It is shown, that one of the conditions of the weakly-collapsing solutions with the zero energy produces the infinite number of the IN functionals identically equal to zero on the regular solutions of the corresponding differential equation. On the parameters {A, C1} plane there exist as the minimum two special lines. The weakly-collapsing solutions with the zero energy are positioned along one of them (A/C1 = 1/6). It is supposed, that the family of weakly-collapsing solutions with the zero energy is positioned also along the second line (A/C1 = αc). In the area of the high parameter values {C1, α = A/C1} there exists the area of the intermediate asymptotics, wherein the amplitude of U function grows in the wide area of the ξ coordinate