Collective variable analysis of the nonlinear Schrödinger equation for soliton molecules in fibers

Abstract

We present a description of soliton molecules in terms of its collective variables namely temporal separation between two consecutive pulses, peak-power of each pulse, center-of-mass, chirp, frequency and phase of the whole molecule. Assuming the Hermite–Gaussian ansatz to represent the temporal profile of the molecule, we derive a set of six differential equations for the evolution of the collective variables in the limit of the bare or variational approximation. Then we perform numerical experiments to confirm the ability of the proposed approach for two-soliton molecule propagating along a Dispersion-managed fiber for anomalous, zero or normal averaged dispersion.