Formulation of mathematical problems in fiber optical telecommunications

Nowadays, more than 90% of data traffic is transmitted through fiber optic communication lines, which is the only way to achieve speeds of tens of terabits per second at a distance of hundreds to thousands of kilometers. Fiber nonlinearity is the main obstacle to further increase of information throughput, so developing algorithms for its mitigation and compensation is very important for telecommunication industry. The report will discuss the mathematical model of light propagation on the fiber and the main approaches to its approximation, based on the Split Step Fourier Method (SSFM) and the Perturbation theory (PBM - perturbation based model). The problem of adaptive nonlinear equalization will also be formulated, and the various objective functions for adapting the model coefficients are considered.