Nonlinear Schrödinger equation in optics

Summary

In optics, the cubic nonlinear Schrödinger equation describes the slowly varying envelope of a light pulse or beam in a medium with the Kerr effect. The distance of propagation plays the role of time, and dispersion or diffraction plays the role of the kinetic term. For pulses in optical fibres it is one-dimensional and integrable, which explains optical solitons. For beams in bulk media it is two-dimensional and describes self-focusing.