Abstract
A theory based on the Kukhtarev-Vinetskii model is developed that provides the evolution equation of one-dimensional optical spatial solitons in photorefractive media. In the steady-state regime and under appropriate external bias conditions, our analysis indicates that the underlying wave equation can exhibit bright and dark as well as gray spatial soliton states. The characteristics of these self-trapped optical beams are discussed in detail. (C) 1995 Optical Society of America

Abstract
Biased photorefractive media are known to admit bright and dark solitons. The bright solitons in these media are always stable, but their dark counterparts are unstable above a certain background intensity and below a critical velocity. We use the stability criterion and the Vakhitov-Kolokolov function to precisely determine the unstable-parameter region. We also predict the strength of the instability by determining the unstable eigenvalues and eigenmodes using the Evans function method. Numerical simulation of the full evolution equation confirms the results.

Abstract
The self-bending process of steady-state bright spatial solitons in biased photorefractive media is investigated by taking into account diffusion effects. By integrating numerically the nonlinear propagation equation, it is found that the soliton beam evolution is approximately adiabatic. The self-deflection process is further studied using perturbation analysis, which predicts that the center of the optical beam moves on a parabolic trajectory and, moreover, that the central spatial frequency component shifts linearly with the propagation distance. Relevant examples are provided.

Abstract
The eruption solitons that exist under the complex cubic-quintic Ginzburg-Landau equation (CGLE) may be eliminated by the introduction of a term that in the optical context represents intrapulse Raman scattering (IRS) The later was observed in direct numerical simulations and here we have obtained the system of ordinary differential equations and the corresponding traveling solitons that replace the eruption solutions In fact we have found traveling solutions for a subset of the eruption CGLE parameter region and a wide range of the IRS parameter However for each set of CGLE parameters they are stable solely above a certain threshold of IRS

Abstract
The complex cubic-quintic Ginzburg-Landau equation (CGLE) admits a special type of solutions called eruption solitons. Recently, the eruptions were shown to diminish or even disappear if a term of intrapulse Raman scattering (IRS) is added, in which case, self-similar traveling pulses exist. We perform a linear stability analysis of these pulses that shows that the unstable double eigenvalues of the erupting solutions split up under the effect of IRS and, following a different trajectory, they move on to the stable half-plane. The eigenfunctions characteristics explain some eruptions features. Nevertheless, for some CGLE parameters, the IRS cannot cancel the eruptions, since pulses do not propagate for the required IRS strength.

Abstract
Ultrashort pulse propagation in fibers is affected by intrapulse Raman scattering (IRS) which causes both a linear frequency downshift and a quadratic displacement of the peak pulse, as functions of the propagation distance. This effect has been known and treated by perturbation methods applied to the nonlinear Schroumldinger equation since the period of intense research on soliton propagation. Here, we find solutions of the model equation using an accelerating self-similarity variable and study their stability. These solutions have Airy function asymptotics which give them infinite energy. For small IRS, the algebraically decaying tail is negligible and these solutions are a very good approximation of the profiles observed in the full equation simulations. For strong IRS (but beyond the regime in which the evolution equation is valid for silica fibers), the self-similar pulses have noticeable left tails exhibiting Airy oscillations. Whenever their truncated forms are used as initial conditions of the full equation, they experience amplitude decay and show left tails that are consistent with radiation escaping from the central pulse. These observations are interpreted as being the effects of a continuum constitution of the infinite left tail.