Among the optical effects that are intensively investigated in recent decades is the phenomenon of self-action of light beams in nonlinear optical media, which is characterized by a refractive index depending on the intensity of the light wave (e.g. self-trapping and self-focusing of optical beams, self-phase modulation of optical pulses etc.). The interaction of the light with a nonlinear material allows to realize the direct optical conversion of images and to control the space-time light structure. The formations of localized spatial structures, so-called optical solitons, which are solutions of the nonlinear differential equations describing such phenomena, are the focus of scientific and practical interest [1-6]. The reason for these intensive studies of solitons is the possibility of their use in modern communication systems, like high-speed systems of fiber-optical information transfer, including self-trapping structure formation due to nonlinear optical effects, creation of waveguiding optical elements with tunable characteristics etc. Owing to diffraction, a collimated beam of light with a diameter d usually spreads with an angle of λ / d. However, already almost 50 years ago it was found that this spreading could be avoided in a nonlinear optical medium, which possesses an intensity-dependent index of refraction that increases with light intensity [7-9]. As a result, the beam forms a dielectric waveguide for itself with solitons as self-trapping solutions. These optical spatial solitons correspond to self-directed beams, which are limited in the across-track direction orthogonal to the direction of propagation [1]. Thereby the natural diffraction divergence of the propagating beam is compensated by the refraction of light when the refractive index is higher in the central part of the beam than at its periphery. The effect of the suppression of the diffraction by the local variation of the refractive index occurs therefore as a result of the exceptional properties of nonlinear media (i.e. the nonlinear increase of the refractive index in a region with higher intensity), leading to the spatial self-focusing of the beam. There is a dynamic balancing between diffraction of the beam and self-focusing due to the nonlinearity of the medium. Since the light wave is captured in an area with higher refractive index, such an area represents a waveguide or self-written channel, thus forming a Chapter 1. Introduction 2 spatial soliton structure. If several of such light channels are formed in parallel, an interaction between them can happen [6]. In other words, solitons propagate and interact with each another while displaying properties that are associated with real particles (quasi-particles).