Double Wronskian solutions of a nonlinear Schrödinger equation in an averaged dispersion-managed fiber system

Abstract

A nonlinear Schrödinger equation in the presence of chirp and loss terms, which describes the optical solitons in an averaged dispersion-managed (DM) fiber system with fiber losses, is studied via symbolic computation. N-soliton solutions are constructed and verified with the Wronskian technique. Analytic one-, two- and three-soliton solutions are discussed. The soliton has a linear frequency chirp. Soliton width increases exponentially while soliton amplitude, energy and speed decrease exponentially along the DM fiber. As the chirp-loss coefficient increases, soliton width gets wider, while soliton amplitude, energy and speed become smaller. Interactions between the two solitons and among the three solitons are discussed and illustrated. For the larger initial soliton separations, interactions result in some smaller envelopes, which soon disappear due to the chirp-loss effect. When the soliton separations almost reaches zero, solitons interact quasi-periodically along the DM fiber, while each soliton undergoes broadening and decaying.