PHYSICAL JOURNAL D c© EDP Sciences

Abstract. A variational technique to deal with nonlinear dissipative pulse propagation is established. By means of a generalization of the Kantorovitch method, suitable for non-conservative systems, we are able to cope with an extended nonlinear Schrödinger equation (NLSE) which describes pulse propagation under the influence of nonlinear loss and/or gain, in particular, in the presence of two-photon absorption (TPA). Based on the characteristics of the exact solution of the NLSE in the absence of TPA, we investigate the eects of frequency dispersion of the nonlinear susceptibility associated to the two-photon resonance, obtaining the necessary conditions for a solitary wave solution, even in the presence of a self-steepening term. PACS. 42.65.-k Nonlinear optics { 03.40.Kf Waves and wave propagation: general mathematical aspects { 52.35.Mw Nonlinear waves and nonlinear wave propagation (including parametric eects, mode coupling, ponderomotive eects, etc.) Variational approaches have gained a new thrust in re-cent years in many branches of science, including quite distinct elds such as correlations in charged polymers [1], sandpile dynamics [2] and excitations of a Bose-Einstei