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Nonlinear Fourier Transforms in Action

Total Cost €


EC-Contrib. €






Project "NEUTRINO" data sheet

The following table provides information about the project.


Organization address
address: STEVINWEG 1
city: DELFT
postcode: 2628 CN

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Netherlands [NL]
 Total cost 1˙337˙907 €
 EC max contribution 1˙337˙907 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-03-01   to  2022-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TECHNISCHE UNIVERSITEIT DELFT NL (DELFT) coordinator 1˙337˙907.00


 Project objective

Nonlinear effects are ubiquitous in many modern technology fields such as photonics and hydromechanical engineering. The standard method to deal with nonlinear effects is to use linear approximations because they are simple to work with. Engineers typically consider nonlinear effects a nuisance that cannot be dealt with in exact terms. This intuition is deeply engrained in the collective subconscious, but it is not always correct -- not all nonlinearities are equally bad. Many practically important nonlinear systems can be approached using so-called nonlinear Fourier transforms, which offer simple closed-form descriptions for nonlinear phenomena that are difficult to work with in the conventional time- or frequency-domain, similar to how the conventional Fourier transform simplifies the analysis of linear systems. Today, almost fifty years after the discovery of the first nonlinear Fourier transform by Gardner et al., nonlinear Fourier transforms have been studied intensively in mathematics and physics. However, despite many potential applications, they have not yet found widespread use in engineering. The lack of efficient numerical algorithms for the computation of nonlinear Fourier transforms similar to the celebrated fast Fourier transform is the major roadblock. I have recently been able to present the first “fast nonlinear Fourier transforms”, but most of this work so far was concerned with signals that obey vanishing boundary conditions. This is the simplest, but not the practically most relevant case. Periodic and Dirichlet boundary conditions occur frequently in practical applications, but their treatment is much more difficult. I aim to push nonlinear Fourier transform into engineering practice by developing fast nonlinear Fourier transforms for two prototypical applications, fiber-optic communications and water-wave data analysis.


year authors and title journal last update
List of publications.
2020 Vinod Bajaj, Shrinivas Chimmalgi, Vahid Aref, Sander Wahls
Exact NFDM Transmission in the Presence of Fiber-Loss
published pages: 1-1, ISSN: 0733-8724, DOI: 10.1109/jlt.2020.2984041
Journal of Lightwave Technology 2020-04-24
2019 Shrinivas Chimmalgi, Peter J. Prins, Sander Wahls
Fast Nonlinear Fourier Transform Algorithms Using Higher Order Exponential Integrators
published pages: 145161-145176, ISSN: 2169-3536, DOI: 10.1109/access.2019.2945480
IEEE Access 7 2019-10-29
2019 Peter J. Prins, Sander Wahls
Soliton Phase Shift Calculation for the Korteweg–De Vries Equation
published pages: 122914-122930, ISSN: 2169-3536, DOI: 10.1109/access.2019.2932256
IEEE Access 7 2019-10-29
2019 Shrinivas Chimmalgi, Sander Wahls
Theoretical Analysis of Maximum Transmit Power in a b-Modulator
published pages: , ISSN: , DOI:
Proceedings of the 45th European Conference on Optical Communication 2019-10-29
2019 Vinod Bajaj, Shrinivas Chimmalgi, Vahid Aref and Sander Wahls
Exact nonlinear frequency division multiplexing in lossy fibers
published pages: , ISSN: , DOI:
Proceedings of the 45th European Conference on Optical Communication 2019-10-29
2018 Tao Gui, Gai Zhou, Chao Lu, Alan Pak Tao Lau, Sander Wahls
Nonlinear frequency division multiplexing with b-modulation: shifting the energy barrier
published pages: 27978, ISSN: 1094-4087, DOI: 10.1364/oe.26.027978
Optics Express 26/21 2019-04-18
2018 Sander Wahls, Shrinivas Chimmalgi, Peter J Prins
FNFT: A Software Library for Computing Nonlinear Fourier Transforms
published pages: 597, ISSN: 2475-9066, DOI: 10.21105/joss.00597
Journal of Open Source Software 3/23 2019-04-18

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