Instabilities of dark solitons

Cubic-Quartic Optical Solitons in Fiber Bragg Gratings with Dispersive Reflectivity Having Parabolic Law of Nonlinear Refractive Index by Lie Symmetry

This work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the governing partial differential equations to the corresponding ordinary differential equations which are subsequently integrated. This integration is conducted using two approaches which are the modified Kudryashov’s approach as well as the generalized Arnous’ scheme. These collectively yielded a full spectrum of cubic-quartic optical solitons that have been proposed to control the depletion of the much-needed chromatic dispersion. They range from bright, dark, singular to combo solitons. These solitons are considered with dispersive reflectivity, which maintains the necessary balance between chromatic dispersion and nonlinear refractive index structure for an uninterrupted transmission of solitons along intercontinental distances. Their respective surface and contour plots are also exhibited. A few closing words are included with some prospective future avenues of research to extend this topic further.

Gray solitons in parity-time symmetric potentials

We numerically study the gray solitons in parity-time (PT) symmetric potentials. Simulated results show that there are two kinds of gray solitons, the dip-shaped gray solitons and the hump-shaped solitons, and both of them can be stable. Hump-shaped solitons can always exist, but the grayness of a stable dip-shaped gray soliton should exceed a threshold value. More interesting, it is discovered that when propagating in PT symmetric potentials, the gray solitons have no transverse deviation, and this is a phenomenon different from the usual gray solitons.

Stable control of pulse speed in parametric three-wave solitons

We analyze the control of the propagation speed of three wave packets interacting in a medium with quadratic nonlinearity and dispersion. We find analytical expressions for mutually trapped pulses with a common velocity in the form of a three-parameter family of solutions of the three-wave resonant interaction. The stability of these novel parametric solitons is simply related to the value of their common group velocity.

Solitons in nonlocal nonlinear media: exact solutions

We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.

Criteria for existence and stability of soliton solutions of the cubic-quintic nonlinear Schrodinger equation

A subset of the soliton solutions of the cubic-quintic nonlinear Schrodinger equation (NLSE) is presented in analytical form. General criteria for existence are expressed in terms of the parameters of the NLSE. The normalized momentum entering the stability criterion is evaluated explicitly.

Drift instability of dark solitons in saturable media

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

Observation of vortex solitons created by the instability of dark soliton stripes

The first experimental observation to the authors' knowledge is reported of the generation of optical vortex solitons from instability and breakup of a dark soliton stripe propagating through a saturable self-defocusing nonlinear medium.

Stability of black solitons in media with arbitrary nonlinearity

It is shown that the black solitons in an optical fiber or a uniform medium with arbitrary nonlinearity are all stable. The conclusion from the analytical stability analysis is consistent with that of numerical simulations. This then dismisses a previous criterion that suggests that the black solitons in a saturable nonlinear medium can be unstable.