Abstract
In the slowly varying envelope approximation we derive the basic equations that describe the propagation of ultrashort pulses in quadratically nonlinear media in which a wave at a fundamental frequency interacts with its second harmonic. In the governing equations we keep linear terms that account for both second- and third-order dispersion and nonlinear terms describing both nonlinear dispersion and self-steepening of the pulse edge. We then perform the Painleve singularity structure analysis of the most general system of coupled partial differential equations we derived. In a specific case, when third-order dispersion is negligible, by using a Hirota-like method, we found zero- and one-parameter families of bright (fundamental frequency) and dark (second harmonic) solitary waves which travel at a locked group velocity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have