Curve Lengthening via Regularized Motion Against Curvature from the Strong FCH Flow

Chen, Yuan; Promislow, Keith

doi:10.1007/s10884-022-10178-7

Cited by 2 publications

(1 citation statement)

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“…Indeed numerical observations show that after self-intersection the dark fronts form cells that engage in a chaotic jostling. Such curvature flow transitions have been studied in dissipative systems such as polymer melts, [2] but their presence in a dispersive system are here-to-for unstudied. The analysis presented here is formal but is complemented with a sharp characterization of the transverse spectrum of the wave which shows that the curvature transition is not associated to any transverse instability of the dark soliton.…”

Section: Introductionmentioning

confidence: 99%

Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System

Promislow,

Ramadan

2024

J Nonlinear Sci

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The parametric nonlinear Schrödinger 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 π-phase shift across a thin interface. We establish a simple mechanism through which the parametric term transitions the normal velocity evolution 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.

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Section: Introductionmentioning

confidence: 99%