LAGRANGIAN APPROACH FOR DARK SOLITONS

We propose a variational formalism for dark solitons based on a nontri vial modification of the standard Lagrangian of the nonlinear Schrodin ger equation. Our approach allows to consider a variety of asymptotica lly nonvanishing localised solutions for applying a variational techni que together with the correct definition of momentum and energy. We de monstrate, on several particular examples, how this variational approa ch works, and we also point out its suitability for more general probl ems, e.g. those involving the analysis of the dark soliton interaction as well as the perturbation-induced dynamics of dark solitons and opt ical vortex solitons.