TY - JOUR
T1 - Instabilities, solitons and rogue waves in PT -coupled nonlinear waveguides
AU - Bludov, Yu V.
AU - Driben, R.
AU - Konotop, V. V.
AU - Malomed, B. A.
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - instabilities
KW - nonlinear Schr̈odinger equation
KW - parity-time symmetry
KW - rogue wave
UR - http://www.scopus.com/inward/record.url?scp=84878882155&partnerID=8YFLogxK
U2 - 10.1088/2040-8978/15/6/064010
DO - 10.1088/2040-8978/15/6/064010
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AN - SCOPUS:84878882155
SN - 2040-8978
VL - 15
JO - Journal of Optics (United Kingdom)
JF - Journal of Optics (United Kingdom)
IS - 6
M1 - 064010
ER -