Mathematical aspects of the theory of guided waves in nonlinear optical fibres

Guided waves in nonlinear optical fibres are modelled as special solutions of Maxwell's equations in an axi-symmetric dielectric medium whose refractive index depends on the intensity of the electric field. I shall present some situations in which the problem can be reduced to a nonlinear eigenvalue problem and then I shall summarise some of the rigorous results that have been obtained and how they relate to the underlying physical problem.