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

• Author(s): Bludov, Yuliy V. ; Driben, R. ; Konotop, Vladimir V. ; Malomed, B. A.
• Date: 2013
• Persistent ID: http://hdl.handle.net/1822/27114
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Parity–time symmetry; Instabilities; Rogue wave; Nonlinear schrödinger equation
• Document Type: Article
• Language: English

Description

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