Instabilities, solitons and rogue waves in PT -coupled nonlinear waveguides

Yu V. Bludov, R. Driben, V. V. Konotop, B. A. Malomed

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83 Scopus citations

Abstract

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time ()-symmetric system of linearly coupled nonlinear Schrödinger equations, which describes a Kerr-nonlinear optical coupler with mutually balanced gain and loss in its cores. Besides the linear coupling, the overlapping cores are coupled through the cross-phase-modulation term too. While the rogue waves, built according to the pattern of the Peregrine soliton, are (quite naturally) unstable, we demonstrate that the focusing cross-phase-modulation interaction results in their partial stabilization. For -symmetric and antisymmetric bright solitons, the stability region is found too, in an exact analytical form, and verified by means of direct simulations.

Original languageEnglish
Article number064010
JournalJournal of Optics (United Kingdom)
Volume15
Issue number6
DOIs
StatePublished - Jun 2013

Keywords

  • instabilities
  • nonlinear Schr̈odinger equation
  • parity-time symmetry
  • rogue wave

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