Bright and dark spatial solitons in non-Kerr media

An overview of the theory of self-guided optical beams, spatial optical solitons supported by non-Kerr non-linearities, is presented. This includes bright and dark solitons in optical media with intensity-dependent non-linear response as well as two-component solitary waves supported by parametric wave mixing in quadratic or cubic media. The properties of non-linear spatially localized waves are discussed for qualitatively different types of soliton bearing non-integrable non-linear models, including the scalar model described by a generalized non-linear Schrödinger equation and the models of the second- and third-harmonic generation. Special attention is paid to the recent advances of the theory of soliton stability and soliton internal modes.