Nonlinear Theory of Soliton Instabilities

We describe the development of solitons instabilities using a multi-scale asymptotic expansion technique valid near the instability threshold. This approach allows us to describe analytically both linear and nonlinear regime of the soliton evolution. Examples considered include: (i) bright solitons supported by non-Kerr nonlinearities, (ii) parametric bright soli-tons in χ(2) optical materials, and (iii) dark solitons in non-Kerr materials.