Searched for: subject%3A%22nonlinear%255C+Fourier%255C+transforms%22
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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
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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
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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
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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
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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
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Chimmalgi, S. (author)
Due to the ever increasing global connectivity, the demand on the fiber-optic communication infrastructure is projected to keep increasing rapidly. A major factor currently limiting transmission capacity is the fiber nonlinearity. Some researchers have suggested the application of nonlinear Fourier transforms to exploit the fiber nonlinearity...
doctoral thesis 2022
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Kitsios, Christos (author)
The nonlinear Fourier transform for the focusing periodic nonlinear Schrodinger equation is investigated. This paper is focused on the approximation of the spines in the nonlinear spectrum using results from Floquet theory. Algorithms for the numerical computation of the spines based on the Fourier collocation method are...
student report 2022
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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
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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
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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
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de Vries, Lianne (author)
Optical fibers form the backbone of our global data transmission infrastructure. As demands on global data transmission grow the capacity of these systems needs to be increased. The behaviour of light waves through these optical fibers is described by the Manakov Equation (ME), a system of nonlinear partial differential equations.<br/><br/>The...
master thesis 2021
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de Koster, P.B.J. (author), Koch, Jonas (author), Pachnicke, Stephan (author), Wahls, S. (author)
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.
conference paper 2021
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Brühl, M. (author), Wahls, S. (author), Barranco Granged, Ignacio (author), Liu, Philipp L.-F. (author)
Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations, and later discrete solitons, is strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the...
conference paper 2020
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Chimmalgi, S. (author), Wahls, S. (author)
The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear bandwidth, signal duration, and power are coupled when singularities in the nonlinear spectrum are...
journal article 2020
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Bajaj, V. (author), Chimmalgi, S. (author), Aref, Vahid (author), Wahls, S. (author)
Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so-called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the...
journal article 2020
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de Koster, P.B.J. (author), Wahls, S. (author)
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....
journal article 2020
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GEZER, GÜROL (author)
As a nonlinear alternative to the linear interpretation of arterial blood pressure waveform, soliton theory has been proposed to model arterial blood pressure by interpreting the pulsatile nature of pressure pulses in the viewpoint of soliton transmission. The existing solitary wave literature supports this interpretation by deriving Korteweg-de...
master thesis 2019
document
Vaibhav, V.K. (author)
We explore two classes of exponential integrators, in this letter, to design the nonlinear Fourier transform (NFT) algorithms with a convergence order of four on an equispaced grid. The integrating factor-based method in the class of the Runge-Kutta methods yields algorithms with complexity O(N\log<sup>2</sup>N) (where N is the number of...
journal article 2019
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de Koster, P.B.J. (author), Wahls, S. (author)
Fibre-optic transceivers based on nonlinear Fourier transforms approximate the link by a lossless path-average model. We propose a new method that identifies a suitable lossless model from time-domain input-output data when fibre parameters are unknown. No special training signals are needed.
conference paper 2019
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Chimmalgi, S. (author), Prins, Peter J. (author), Wahls, S. (author)
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of highly accurate low-complexity algorithms remains a challenge. In this paper, we present new fast forward NFT...
journal article 2019
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