Solitary waves and two-photon absorption

Investigations on pulse propagation near the half band gap of semiconductors, where a two-photon resonant enhanced nonlinearity takes place, indicate asymmetric frequency spectra together with self-steepening of the transmitted pulse. These features are attributed to the frequency dispersion of the nonlinear refractive index coefficient and also to the coefficient of two-photon absorption. Lately there has been considerable interest on such investigations for all-optical switching applications, so that, in this paper we investigate an extended version of the nonlinear Schrodinger equation (NLSE) including a self-steepening term, which takes into account the frequency dispersion of the nonlinear susceptibility and also a nonlinear absorptive term. To this end we employ a recently devised variational approach suitable to deal with nonlinear dissipative propagation and show the existence of a solitary wave as a result of the interplay among the various effects considered