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.

Abstract
The effects of third-order dispersion (TOD) and intrapulse Raman scattering (IRS) on the erupting solitons of the complex cubic-quintic Ginzburg-Landau equation are investigated by direct numerical simulations and linear stability analysis. Our results indicate that positive TOD eliminates eruptions on the leading edge of the soliton, whereas negative TOD cancels them on the other side. Moreover, the combined action of TOD and IRS is in certain cases able to eliminate explosions on both sides of the soliton, at much lower IRS values than with IRS alone. The profiles of the stationary solutions are increasingly asymmetric with TOD, and their velocity varies almost linearly with IRS. (C) 2012 Published by Elsevier B.V.

Abstract
We show that incoherently coupled soliton pairs are possible in biased photorefractive crystals, under steady-state conditions. These solitons can propagate in bright-bright, dark-dark, as well as in bright-dark configurations. Such soliton pairs can be established provided that the carrier beams share the same polarization, wavelength, and are mutually incoherent. Relevant examples are provided where the photorefractive crystal is of the strontium barium niobate type. The characteristics and stability properties of these soliton states are also discussed in detail. © 1996 American Institute of Physics.