Eur. Phys. J. Special Topics 147, 253-264 (2007)
https://doi.org/10.1140/epjst/e2007-00212-x

The Maxwell-Lorentz model for optical pulses

¹ Department of Mathematics, Technical University of Denmark, Matematiktorvet, Bldg. 303, 2800 Kongens Lyngby, Denmark
² Department of Mathematics, Arizona Center for Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA

Abstract

Dynamics of optical pulses, especially of ultra short femtosecond pulses, are of great technological and theoretical interest. The dynamics of optical pulses is usually studied using the nonlinear Schrödinger (NLS) equation model. While such approach works surprisingly well for description of pulse propagation, at least in the femtosecond regime, the full system posses a wealth of new wave phenomena that we explore in this paper: envelope collapse regularization resulting in the orignal pulse splitting; development of infinite gradients in the carrier wave; existence of the stable top hat traveling wave solutions formed by a pair of kink anti-kink shaped optical waves.