- document
-
de Koster, P.B.J. (author), Wahls, S. (author)Lax-integrable partial differential equations (PDEs) can by definition be described through a compatibility condition between two linear operators. These operators are said to form a Lax pair for the PDE, which itself is usually nonlinear. Lax pairs are a very useful tool, but unfortunately finding them is a difficult problem in practice. In...journal article 2024
- document
-
Lee, Y.C. (author), Brühl, M. (author), Doong, Dong Jiing (author), Wahls, S. (author)Rogue waves are sudden and extreme occurrences, with heights that exceed twice the significant wave height of their neighboring waves. The formation of rogue waves has been attributed to several possible mechanisms such as linear superposition of random waves, dispersive focusing, and modulational instability. Recently, nonlinear Fourier...journal article 2024
- document
-
Bajaj, V. (author), Van de Plas, Raf (author), Wahls, S. (author)While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1] (Cho and Winzer, 2009), it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms...journal article 2024
- document
-
Lee, Y.C. (author), Brühl, M. (author), Wahls, S. (author)When a large number of solitons dominates the dynamics of a system, scientists describe this collective behaviour of solitons as a soliton gas. Soliton gases are currently the subject of intense practical and theoretical investigations. The existence of soliton gases has been confirmed in experiments, but is not clear what kind of sea states...conference paper 2023
- document
-
Aamir, S. (author), Wahls, S. (author)Recently, a novel parameter identification method for partial differential equations based on the Koopman operator framework has been proposed. We evaluate its suitability for the identification of single span optical fiber links of various lengths in simulations.conference paper 2023
- document
-
de Koster, P.B.J. (author), Wahls, S. (author)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 which the computation typically becomes prohibitively expensive and/or numerically unstable. We partition the full signal in both frequency and time to obtain...journal article 2023
- document
-
Teutsch, Ina (author), Brühl, M. (author), Weisse, Ralf (author), Wahls, S. (author)The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the...journal article 2023
- document
-
de Koster, P.B.J. (author), Schulz, Olaf (author), Koch, Jonas (author), Pachnicke, Stephan (author), Wahls, S. (author)We experimentally investigate the problem of monitoring the Kerr-nonlinearity coefficient $\gamma$ from transmitted and received data for a single-mode fiber link of 1600 km length. We compare the accuracy and speed of three different approaches. First, a standard split-step Fourier method is used to predict the output at various $\gamma$...journal article 2023
- document
-
Chimmalgi, S. (author), Wahls, S. (author)Riemann theta functions play a crucial role in the field of nonlinear Fourier analysis, where they are used to realize inverse nonlinear Fourier transforms for periodic signals. The practical applicability of this approach has however been limited since Riemann theta functions are multi-dimensional Fourier series whose computation suffers...journal article 2023
- document
-
Brühl, M. (author), Prins, Peter J. (author), Ujvary, Sebastian (author), Barranco, Ignacio (author), Wahls, S. (author), Liu, Philip L.-F. (author)In this paper, we study the propagation of bores over a long distance. We employ experimental data as input for numerical simulations using COULWAVE. The experimental flume is extended numerically to an effective relative length of x/h=3000, which allows all far-field solitons to emerge from the undular bore in the simulation data. We apply the...journal article 2022
- document
-
Bajaj, V. (author), Buchali, Fred (author), Chagnon, Mathieu (author), Wahls, S. (author), Aref, Vahid (author)High-symbol-rate coherent optical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. Recently, we proposed in [20] a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128...journal article 2022
- document
-
Prins, Peter J. (author), Wahls, S. (author)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 as part of the Non-linear Fourier Transform (NFT) for the KdV equation. The algorithm that we propose makes use of Sturm-Liouville (SL) oscillation theory to guaranty...journal article 2022
- document
-
Masoumi, H. (author), Myers, N.J. (author), Leus, G.J.T. (author), Wahls, S. (author), Verhaegen, M.H.G. (author)Fast millimeter wave (mmWave) channel estimation techniques based on compressed sensing (CS) suffer from low signal-to-noise ratio (SNR) in the channel measurements, due to the use of wide beams. To address this problem, we develop an in-sector CS-based mmWave channel estimation technique that focuses energy on a sector in the angle domain....conference paper 2022
- document
-
Bajaj, V. (author), Van de Plas, Raf (author), Aref, Vahid (author), Wahls, S. (author)We propose a novel method for blind polarization-demultiplexing of probabilistically shaped signals for coherent receivers. The method is capable of separating signals with (quasi) Gaussian distributions by exploiting temporal correlations added to the transmit signals. The proposed method is evaluated in challenging mixing scenarios.conference paper 2022
- document
-
de Koster, P.B.J. (author), Koch, Jonas (author), Schulz, Olaf (author), Pachnicke, Stephan (author), Wahls, S. (author)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.conference paper 2022
- document
-
Wahls, S. (author)We present the first method for the joint modulation of the continuous and the discrete nonlinear Fourier spectrum of finite duration signals.conference paper 2022
- document
-
de Koster, P.B.J. (author), Brühl, M. (author), Wahls, S. (author)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...conference paper 2022
- document
-
Zhang, H. (author), Wahls, S. (author), Brühl, M. (author)In the past decade, observations in the German estuaries such as the rivers Elbe and Weser show increasingly serious damage to bank protection structures (groins and revetments). This damage is caused mainly by waves induced by the passing of big container ships in the shallow and narrow maritime waterways. These ship-induced 3D wave fields...conference paper 2021
- document
-
Zhang, H. (author), Wahls, S. (author), Brühl, M. (author)In the past decade, observations in the German estuaries such as the rivers Elbe and Weser show increasingly serious damage to bank protection structures (groins and revetments). This damage is caused mainly by waves induced by the passing of big container ships in the shallow and narrow maritime waterways. These ship-induced 3D wave fields...conference paper 2021
- document
-
Prins, Peter J. (author), Wahls, S. (author)We present an algorithm to compute the N-fold Crum transform (also known as the dressing method) for the Korteweg–de Vries equation (KdV) accurately in floating point arithmetic. This transform can be used to generate solutions of the KdV equation, e.g. as a part of the inverse Non-linear Fourier Transform. Crum transform algorithms that...journal article 2021