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arXiv · 1304.7369

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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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 (PT)-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 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 PT-symmetric and antisymmetric bright solitons, the stability region is found too, in an exact analytical form, and verified by means of direct simulations.

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Yu. V. Bludov, R. Driben, V. V. Konotop, B. A. Malomed. 2013-04-27. Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides. https://doi.org/10.1088/2040-8978%2F15%2F6%2F064010

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