Strong Phase Correlations of Solitons of Nonlinear Schrödinger Equation

Abstract

We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schrödinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to $q$-deformed Hopf algebra with deformation parameter $q$ being the fourth root of unity makes the values of the Chern-Simons term coefficient, $k=2$, and of the coupling constant, $g=1/2$, fixed; no collapsing solutions are present at those values.