ar X iv : h ep - t h / 94 10 10 2 v 1 1 4 O ct 1 99 4 Quasiperiodic Solutions of the Fibre Optics Coupled Nonlinear Schrödinger Equations

ar X iv : h ep - t h / 92 10 08 3 v 1 1 5 O ct 1 99 2 QUASI - PERIODIC SOLUTIONS FOR MATRIX NONLINEAR SCHRÖDINGER EQUATIONS

The Adler-Kostant-Symes theorem yields isospectral hamiltonian flows on the dual˜g + * of a Lie subalgebrã g + of a loop algebrã g. A general approach relating the method of integration of Krichever, Novikov and Dubrovin to such flows is used to obtain finite-gap solutions of matrix Nonlinear Schrödinger Equations in terms of quotients of θ-functions.

ar X iv : h ep - t h / 94 10 05 5 v 1 9 O ct 1 99 4 RESOLUTION OF DIAGONALS AND MODULI SPACES

ar X iv : h ep - t h / 95 10 11 4 v 1 1 7 O ct 1 99 5 Spinors in non - relativistic Chern - Simons electrodynamics

It is shown that the non-relativistic 'Dirac' equation of Lévy-Leblond, we used recently to describe a spin 1 2 field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from 3 + 1 dimensions. This allows us to prove that the system is Schrödinger symmetric. A spinor representation of the Schrödinger group is presented. Static, self-dual solu...

ar X iv : h ep - t h / 94 10 19 9 v 1 2 6 O ct 1 99 4 Linear Connections on the Quantum Plane

A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.

ar X iv : s ol v - in t / 9 90 40 17 v 1 1 6 A pr 1 99 9 QUASI - PERIODIC AND PERIODIC SOLUTIONS FOR SYSTEMS OF COUPLED NONLINEAR SCHRÖDINGER EQUATIONS

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibers with strong birefingence and two-mode optical fibers. Recently these equations appear as model, which describe pulse-pulse interaction in wavelength-division-multiplexed channels of optical fiber transmissi...