Abstract
We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. The separation of initially nearby trajectories in the asymptotic limit is predominantly used to distinguish qualitatively between time-periodic behavior and chaotic localized states. These results are further corroborated by Fourier transforms and time series. Quasiperiodic behavior is obtained as well, but typically over a fairly narrow range of parameter values. For illustration, two examples of nonlinear gradient terms are examined: the Raman term and combinations of the Raman term with dispersion of the nonlinear gain. For small quintic perturbations, it turns out that the chaotic localized states are showing a transition to periodic states, stationary states, or collapse already for a small magnitude of the quintic perturbations. This result indicates that the basin of attraction for chaotic localized states is rather shallow.

Abstract
We show that the evolution equations describing the two-wave mixing interaction between two co-directional optical beams in photorefractive media can allow spatial shock-wave solutions. The properties of this new family of kink-type wave fronts are described in detail. © 2001 OSA/NLGW 2001, © 2000 Optical Society of America.

Abstract
VITRUVsim is a numerical tool with as much as possible physics included. Inputs are the source parameters (flux, morphology, position...) and outputs are sequences of observed fringes and/or reduced visibilities. VITRUVsim is written in a portable and free language Yorick(4).

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.