Similaritons in nonlinear optical systems

By using the lens-type transformation, we find the self-similar evolution of four kinds of optical similaritons in (1+1)-dimensional nonlinear Schrodinger equations. They are the exact solitonic similaritons, quasi solitonic similaritons, asymptotic compact parabolic similaritons and asymptotic Hermite-Gaussian similaritons. Moreover, the interaction of multiple solitonic similaritons are investigated. Approximate but highly accurate analytical methods are developed to describe their center-of-mass motion.