Abstract
We show that the vector beam evolution equations in properly oriented biased photorefractive media can exhibit bright-dark soliton pair solutions under steady-state conditions. These wave pairs are obtained perturbatively provided that the intensities of the two optical beams are approximately equal. Our analysis indicates that these bright-dark vector solitons exist irrespective of the polarity of the external bias field. The stability of these vector pairs has been investigated numerically and it has been found that they are stable only in the regime of positive bias polarity.

Abstract
The modulational instability of quasi-plane-wave optical beams in biased photorefractive media is investigated under steady-state conditions. The spatial. growth rate of the sideband perturbations is obtained by globally treating the space-charge field. Our analysis indicates that the growth rates depend on the strength of the externally applied electric field and, moreover, on the ratio of the optical beam's intensity to that of the dark irradiance. Our results are then compared to previous local treatments of the space-charge field equation. The two approaches are found to be in good agreement in the low spatial-frequency regime provided that the external bias field is sufficiently high. Conversely, in the high spatial-frequency region notable differences may exist. Relevant examples are provided.

Abstract
New types of finite energy Airy beams are proposed. We consider two different types of beams, namely, beams that are obtained as blocked and exponentially attenuated versions of Airy functions Ai and Bi, and beams of finite width but having the Airy functions typical phase. All of them show very interesting properties, such as parabolic trajectories for longer propagation distances, profile evolution exhibiting less diffraction, or better definiteness of the main peak, when compared with other finite energy Airy beams studied before. (C) 2010 Optical Society of America

Abstract
The propagation of bound soliton pairs in nonlinear photonic crystal fibers has recently been experimentally observed. The system may be modeled by a generalized nonlinear Schrodinger equation (GNLSE) which includes higher intrapulse Raman Scattering, self-steepening and higher order dispersion. Here, we find multihumped pulses as result of an accelerating similarity reduction of a GNLSE containing the intrapulse Raman scattering. Numerical simulations of the suitable GNLSE using these solutions as input showed that they are not stable, however, they may be related with the experimentally observed bound pairs since they propagate steadily for distances compared to the ones observed.

Abstract
We investigate the effects of diffusion on the evolution of steady-state dark and gray spatial solitons in biased photorefractive media. Numerical integration of the nonlinear propagation equation shows that the soliton beams experience a modification of their initial trajectory, as well as a variation of their minimum intensity. This process is further studied using perturbation analysis, which predicts that the center of the optical beam moves along a parabolic trajectory and, moreover, that its minimum intensity varies linearly with the propagation distance, either increasing or decreasing depending on the sign of the initial transverse velocity. Relevant examples are provided.

Abstract
We show that the evolution equations describing the two-wave mixing interaction between two codirectional optical beams in photorefractive media can allow spatial shock-wave solutions. Our analysis indicates that these kink-type wavefronts move together at an angle that falls outside the initial +/- theta sector of propagation. The apparent direction of propagation and the spatial widths of these optical shock-wave beams are directly related to their relative intensity.