ON A COUPLED SYSTEM OF EQUATIONS DESCRIBING PULSE-PROPAGATION IN QUADRATIC MEDIA

In the slowly varying envelope approximation we derive the basic equat ions that describe the propagation of ultrashort purses in quadratical ly nonlinear media in which a wave at a fundamental frequency interact s with its second harmonic. In the governing equations we keep linear terms that account for both second-and third-order dispersion and nonl inear terms describing both nonlinear dispersion and self-steepening o f the purse edge. We then perform the Painleve singularity structure a nalysis of the most general system of coupled partial differential equ ations we derived. In a specific case, when third-order dispersion is negligible, by using a Hirota-like method, we found zero-and one-param eter families of bright (fundamental frequency) and dark (second harmo nic) solitary waves which travel at a locked group velocity.