Efficient fiber-optic communication requires precise knowledge of the fiber coefficients, but these often change over time due to factors such as aging or bending. We propose a novel algorithm that identifies the average second-order dispersion and Kerr nonlinearity coefficient of a fiber, without employing any special training signals. Instead, ordinary input and output data recorded during normal operation is used. To the best of our knowledge, this is the first such algorithm. The algorithm is based on the nonlinear Fourier spectrum of the signal, which is known to evolve trivially as the signal propagates through an idealized model of the fiber. The algorithm varies the values of the fiber coefficients until the corresponding nonlinear Fourier spectrum at transmitter and receiver match optimally. We test the algorithm on simulated transmission data over a 1600 km link, and accurately identify the fiber coefficients. The identification algorithm is in particular well suited for providing a fiber model for nonlinear Fourier transform-based communication.

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to so-called 'grid-crossing errors' when particles cross element boundaries. Previous research has shown that B-spline MPM (BSMPM) is a viable alternative not only to MPM, but also to more advanced versions of the method that are designed to reduce the grid-crossing errors. In contrast to many other MPM-related methods, BSMPM has been used exclusively on structured rectangular domains, considerably limiting its range of applicability. In this paper, we present an extension of BSMPM to unstructured triangulations. The proposed approach combines MPM with C 1 -continuous highorder Powell-Sabin (PS) spline basis functions. Numerical results demonstrate the potential of these basis functions within MPM in terms of grid-crossing-error elimination and higher-order convergence.

First experimental results on the characterisation of the nonlinear fibre coefficient using nonlinear Fourier transforms are reported for a 1000 km NZDSF fibre link. No special training signals were used. Instead, conventional pulse-shaped QPSK symbols were transmitted.

Recently, a nonlinear Fourier transform-based Kerr-nonlinearity identification algorithm was demonstrated for a 1000 km NZDSF link with accuracy of 75%. Here, we demonstrate an accuracy of 99% over 1600 km SSMF. Reasons for improved accuracy are discussed.

We propose a novel method to determine the average water depth from shallow, weakly nonlinear water waves that are approximated by the Korteweg-de Vries equation. Our identification method only requires free-surface measurements from two wave gauges aligned in the direction of wave propagation. The method we propose is based on comparing solitonic components in wave packets, which are computed using the nonlinear Fourier transform (NFT) (typical time-series data often contains at least some solitonic components, even when these components are not directly visible). When the correct water depth is used for the normalisation of the wave, the solitonic components found by the NFT remain constant as the wave packet propagates, whereas any other water depth will result in solitonic components that do not remain constant. The basic idea is thus to iteratively determine the water depth that leads to a best fit between the solitonic components of time series measurements at two different gauge positions. We present a proof-of-concept on experimental bore data generated in a wave flume, where the identified water depth is within 5% of the measured value.