N ov 2 00 5 About nonlinear geometric optics

5 N ov 2 00 1 Reductions of N - wave interactions related to low – rank simple Lie algebras . I : Z 2 – reductions

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the second order reductions of the N–wave interactions related to low–rank simple Lie algebras g can be embedded also in the Weyl group of g. This allows us to display along with the well known ones a number o...

6 N ov 2 00 3 The nonlinear directional coupler . An analytic solution

Linear and nonlinear directional couplers are currently used in fiber optics communications. They may also play a role in multiphoton approaches to quantum information processing if accurate control is obtained over the phases and polarizations of the signals at the output of the coupler. With this motivation, the constants of motion of the coupler equation are used to obtain an explicit analyt...

ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

N ov 2 00 4 February 1 , 2008 DIRAC - HARMONIC MAPS

We introduce a functional that couples the nonlinear sigma model with a spinor field: L = ∫ M [|dφ|2 + (ψ,D/ψ)]. In two dimensions, it is conformally invariant. The critical points of this functional are called Dirac-harmonic maps. We study some geometric and analytic aspects of such maps, in particular a removable singularity theorem.

ar X iv : a st ro - p h / 01 11 13 6 v 1 7 N ov 2 00 1 1 Active Optics in Modern , Large Optical Telescopes