Nonautonomous Solitons in the (3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We discuss the nonlinear Schrödinger equation with variable coefficients in 2D graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on these solutions, we mainly investigate the dynamical behaviors of solitons in three different diffraction decreasing waveguides with the hyperbolic, Gaussian and Logarithmic profiles. Results indicate that for the same parameters, the amplitude of bright solitons in the Logarithmic profile and the amplitude of dark solitons in the Gaussian profile are biggest respectively, and the amplitude in the hyperbolic profile is smallest, while the width of solitons has the opposite case.

Section: Introductionmentioning

confidence: 99%

Spatial Solitons in 2D Graded-Index Waveguides with Different Distributed Transverse Diffractions

Chen¹

2014

Exact Solutions of the Two-Dimensional Cubic-Quintic Nonlinear Schrödinger Equation with Spatially Modulated Nonlinearities

Song¹,

Li²

2013

Applying the similarity transformation, we construct the exact vortex solutions for topological charge S ≥ 1 and the approximate fundamental soliton solutions for S = 0 of the two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and harmonic potential. The linear stability analysis and numerical simulation are used to exam the stability of these solutions. In different profiles of cubic-quintic nonlinearities, some stable solutions for S ≥ 0 and the lowest radial quantum number n = 1 are found. However, the solutions for n ≥ 2 are all unstable.

Nonautonomous Dark Solitons and Rogue Waves in a Graded-Index Grating Waveguide

Liu¹,

Yang²,

Yang³

et al. 2013

We analytically present a family of nonautonomous dark solitons and rogue waves in a planar graded-index grating waveguide with an additional long-period grating. The dark solitons whose dynamics described by the explicit expressions such as the valley, background and wave central position are investigated. We find that dark soliton's depth and the long-period grating have effects on soliton's wave central position; the gain or loss term affects directly both the background and valley of the soliton. For rogue waves, it is reported that one can modulate the distribution of the light intensity by adjusting the parameters of the long-period grating. Additionally, more rogue waves with different evolution behaviors in this special waveguide are demonstrated clearly.