Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation

L. A. Cisneros-Ake, R. Carretero-González, P. G. Kevrekidis, B. A. Malomed

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schrödinger equation with hyperbolic dispersion, under the action of transverse perturbations. We start by discussing a recently proposed adiabatic-invariant approximation for transverse instabilities and its limitations in the bright soliton case. We then focus on a variational approximation used to reduce the dynamics of the bright-soliton stripe to effective equations of motion for its transverse shift. The reduction allows us to address the stripe's snaking instability, which is inherently present in the system, and follow the ensuing spatiotemporal undulation dynamics. Further, introducing a channel-shaped potential, we show that the instabilities (not only flexural, but also those of the necking type) can be attenuated, up to the point of complete stabilization of the soliton stripe.

Original languageEnglish
Pages (from-to)268-281
Number of pages14
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume74
DOIs
StatePublished - 30 Jul 2019

Keywords

  • Bright solitons
  • Filament dynamics
  • Variational approximation

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