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

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.