Analytical solutions of the nonlinear Schrodinger equation with gain [optical solitons]

Summary form only given. The one-dimensional nonlinear Schrodinger equation (NLSE) with gain, and its complex generalization to the Ginzburg-Landau equation have a wide range of applications in nonlinear optics. This paper discusses solutions appropriate to three different propagation regimes and the applications of these solutions. All of these solutions have the common feature of describing self similar solitary wave pulse propagation. The self similar propagating pulses have a linear chirp, and their shape remains mathematically the same, only the amplitude and width scale under the influence of the NLSE during propagation. This is to be contrasted with the well known chirp free fundamental soliton solution of the NLSE which has a strictly constant shape.