Ilya Kuk: Perturbation theory, integrability, and data-driven modeling for fiber optics

First, we treat the weak nonlinearity regime of the Nonlinear Schrödinger equation with perturbation theory: we derive leading corrections to pulse evolution, quantify distortion growth with distance, and compare the predictions with simulations. Second, we address data recovery at higher powers by writing the inverse problem as an affine map from the measured Lax spectrum at the fiber output to the transmitted bit sequence. Simulations show that the continuous spectrum alone suffices for accurate recovery for certain types of signal, so the discrete (soliton) part can be ignored.