#### Condensed Matter Theory

### Maciej Janowicz et.al.: Sub- and superluminal kink-like waves in the kinetic limit of Maxwell-Bloch equations

**Author(s)**:**Maciej Janowicz, Martin Holthaus****Title**:**Date of Upload**: 2011-01-04
**Article**:**J. Phys. A: Math. Theor. 44 025301 (2011), IOP****Keywords**:**PACS**: 05.45.YvSolitons, 02.30.Jr**MSC**: 37K40, 35Q51**Abstract**:- Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level MaxwellBloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the LambertBeer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.
**DOI:**10.1088/1751-8113/44/2/025301

**Sub- and superluminal kink-like waves in the kinetic limit of Maxwell-Bloch equations**

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