Exact self-similar solitary waves and collisions in nonlinear optical media

This paper analyses bright and dark spatial self-similar waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities.It finds an appropriate transformation for the first time such that the nonlinear Schro¨dinger equation (NLSE) with varying coefficients transform into standard NLSE.It obtains one-solitonlike,two-solitonlike and multi-solitonlike self-similar wave solutions by using the transformation.Furthermore,it analyses the features of the self-similar waves and their collisions.