Theory of direct scattering transform for nonlinear wave fields containing solitons is revisited
to overcome fundamental difficulties hindering its stable numerical implementation. With the …

We consider the model of the focusing one-dimensional nonlinear Schrödinger equation
(fNLSE) in the presence of an unstable constant background, which exhibits coherent …

The nonlinear Fourier transform (NFT) is used to characterize the optical combs in the
Lugiato-Lefever equation with both anomalous and normal dispersion. We demonstrate that …

We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat
problem, based on moving in the complex plane along the argument jumps of the function a …

The direct Zakharov–Shabat scattering problem has recently gained significant attention in
various applications of fiber optics. The development of accurate and fast algorithms with …

The nonlinear Schrödinger equation (NLSE) is widely used in telecommunication
applications, since it allows one to describe the propagation of pulses in an optical fiber …

We combine the nonlinear Fourier transform (NFT) signal processing with machine learning
methods for solving the direct spectral problem associated with the nonlinear Schrödinger …

A neural network architecture is proposed that allows a continuous nonlinear spectrum of
optical signals to be predicted and an inverse nonlinear Fourier transform (NFT) to be …

We present a fast method to calculate the significantly large solitonic components of signals
with large time-bandwidth products governed by the nonlinear Schrödinger equation, for …

We propose a numerical algorithm that computes the eigenvalues of the Korteweg–de Vries
equation (KdV) from sampled input data with vanishing boundary conditions. It can be used …