Curvature and Chaos in the Defocusing Parameteric Nonlinear Schrodinger System

TL;DR

This paper investigates how curvature influences the dynamics of dark-soliton fronts in the defocusing parametric nonlinear Schrödinger system, revealing transitions from curvature-driven flow to chaotic motion depending on parametric strength.

Contribution

It derives a normal velocity law for curved dark-soliton fronts and shows how parametric strength causes a transition from curvature-driven shrinking to chaotic interface growth.

Findings

Normal velocity law for dark-soliton fronts derived

Transition from curvature-driven flow to chaos identified

Chaotic motion occurs with strong parametric forcing

Abstract

The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a $\pi$-phase shift across a thin interface. We establish that depending upon the strength of parametric term the normal velocity evolution can transition from a curvature driven flow to motion against curvature regularized by surface diffusion of curvature. In the former case interfacial length shrinks, while in the later the interface length generically grows until self-intersection followed by a transition to chaotic motion.