Prerequisites: 0512.2525 - Electromagnetic fields.

                     0509.2846 -  Partial Differential Equations 

Light propagation in optical fibers, bulk and planar waveguides, and Bragg gratings; dispersion and diffraction. Fundamental nonlinearities in optical media, of the Kerr (cubic) and second-harmonic generating (quadratic) types. Fundamental mathematical models: nonlinear Schroedinger equations and systems of coupled equations. Continuous-wave (uniform) states, modulational instability, and the collapse in multidimensional nonlinear media. Temporal and spatial solitons; solitons in optical fibers; polarization and bimodal propagation. Solitons in dual-core couplers and waveguiding arrays; discrete solitons. Introduction to the method of the inverse scattering transform and integrability. Solitons in nonintegrable systems and variational approximation; dispersion management; interactions between solitons and bound states. The potential use of solitons in telecommunications and data-processing schemes. Parametric solitons in media with the quadratic nonlinearity. Gap solitons in gratings structures. Multidimensional, spatiotemporal, and vortical solitons. Solitons in dissipative media and laser cavities; Ginzburg-Landau equations as fundamental models of dissipative optical media.