Solitons for the (3 + 1)-dimensional coupled nonlinear Schrödinger equations in the inhomogeneous parity-time-symmetric coupler with gain or loss

Xiao-Yu Wu; Bo Tian; Xi-Yang Xie; Jun Chai; He Li; Yan Jiang

doi:10.1117/1.OE.56.8.086108

22 August 2017 Solitons for the (3 + 1)-dimensional coupled nonlinear Schrödinger equations in the inhomogeneous parity-time-symmetric coupler with gain or loss

Xiao-Yu Wu, Bo Tian, Xi-Yang Xie, Jun Chai, He Li, Yan Jiang

Author Affiliations +

Optical Engineering, Vol. 56, Issue 8, 086108 (August 2017). https://doi.org/10.1117/1.OE.56.8.086108

Abstract

Under investigation is the (3+1)-dimensional coupled nonlinear Schrödinger equations, which describe the propagation of the soliton in the inhomogeneous parity-time (PT)-symmetric coupler with gain or loss. Employing the Hirota method and symbolic computation, we obtain the one- and two-soliton solutions under a variable-coefficient constraint. Bäcklund transformation and the corresponding one-soliton solutions are derived. Via graphic analysis, we observe the linear-, parabolic-, and periodic-shaped solitons with different values of the self-phase modulation and cross-phase modulation. Increase of the diffraction and dispersion leads to the increase of both the soliton amplitudes and the velocities. However, ϱ(z) and γ do not affect the soliton amplitude and velocity, with ϱ(z) being the coupling between the modes propagating in the two fibers and γ describing the PT-balanced gain or loss.

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Xiao-Yu Wu, Bo Tian, Xi-Yang Xie, Jun Chai, He Li, and Yan Jiang "Solitons for the (3 + 1)-dimensional coupled nonlinear Schrödinger equations in the inhomogeneous parity-time-symmetric coupler with gain or loss," Optical Engineering 56(8), 086108 (22 August 2017). https://doi.org/10.1117/1.OE.56.8.086108

Received: 4 May 2017; Accepted: 18 July 2017; Published: 22 August 2017

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