ar X iv : 0 90 6 . 34 73 v 1 [ nl in . P S ] 1 8 Ju n 20 09 Fast electromagnetic response of a thin film of resonant atoms with permanent dipole

ar X iv : n lin / 0 50 70 64 v 1 [ nl in . P S ] 2 8 Ju l 2 00 5 Optical transparency modes in anisotropic media

The modes of nonlinear propagation of the two-component electromagnetic pulses through optically uniaxial media containing resonant particles are studied. The features of their manifestation in the " dense " media and in the media with expressed positive and negative birefringences are discussed. It is shown that exponentially and rationally decreasing solutions of the system of material and wa...

ar X iv : n lin / 0 70 20 35 v 1 [ nl in . P S ] 1 6 Fe b 20 07 1 Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings

The propagation of solitary waves in a Bragg grating formed by an array of thin nanostructured dielectric films is considered. A system of equations of Maxwell-Duffing type and describing forward-and backward-propagating waves in such a grating, is derived. Exact solitary wave solutions are found, analyzed, and compared with the results of direct numerical simulations. The last decade has been ...

ar X iv : 0 90 6 . 32 38 v 1 [ m at h . N T ] 1 7 Ju n 20 09 GEOMETRIC AND p - ADIC MODULAR FORMS OF HALF - INTEGRAL WEIGHT by Nick

ar X iv : 0 90 6 . 33 09 v 1 [ m at h . A P ] 1 8 Ju n 20 09 ricci flow of negatively curved incomplete surfaces

We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.

ar X iv : 0 90 6 . 18 57 v 1 [ m at h . C O ] 1 0 Ju n 20 09 On the circumference , connectivity and dominating cycles

Every 4-connected graph with minimum degree δ and connectivity κ either has a cycle of length at least 4δ − 2κ or has a dominating cycle.