FNFT: A software library for computing nonlinear Fourier transforms

Journal article (2018)

Authors

S. Wahls Team Sander Wahls - Mechanical, Maritime and Materials Engineering
S. Chimmalgi Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
Peter J. Prins Team Sander Wahls - Mechanical, Maritime and Materials Engineering
Research Group
Team Sander Wahls (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2018 S. Wahls, S. Chimmalgi, Peter J. Prins
DOI: https://doi.org/10.21105/joss.00597
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Published Date

2018

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sander Wahls

Abstract

The conventional Fourier transform was originally developed in order to solve the heat equation, which is a standard example for a linear evolution equation. Nonlinear Fourier transforms (NFTs)1 are generalizations of the conventional Fourier transform that can be used to solve certain nonlinear evolution equations in a similar way (Ablowitz et al. 1974). An important difference to the conventional Fourier transform is that NFTs are equationspecific. The Korteweg-de Vries (KdV) equation (Gardner et al. 1967) and the nonlinear Schroedinger equation (NSE) (Shabat and Zakharov 1972) are two popular examples for nonlinear evolution equations that can be solved using appropriate NFTs.