Strong Phase Correlations of Solitons of Nonlinear Schr\"odinger Equation

TL;DR

This paper explores how strong phase correlations governed by gauge theory can prevent collapse in 2+1 D nonlinear Schrödinger equations, identifying specific algebraic conditions that eliminate collapsing solutions.

Contribution

It introduces a gauge theory approach based on q-deformed Hopf algebra to suppress collapse in nonlinear Schrödinger equations, fixing key parameters to prevent singularities.

Findings

Collapse is suppressed at specific algebraic parameter values.

Invariance under q-deformed Hopf algebra fixes the Chern-Simons coefficient and coupling constant.

No collapsing solutions exist at the identified parameter values.

Abstract

We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schr\"odinger 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.