Non-Lagrangian collective variable approach for optical solitons in fibres

We use a non-Lagrangian method to express the generalized nonlinear Schrödinger equation, for pulse propagation in optical fibres, in terms of the pulse parameters, called collective variables, such as the pulse width, amplitude, chirp and frequency. The collective variable equations of motion, which include the important effects due to fibre losses, third-order dispersion, stimulated Raman scattering and self-steepening are derived using a direct averaging method without the help of any Lagrangian.