FNFT: A software library for computing nonlinear Fourier transforms
Sander Wahls (TU Delft - Mechanical Engineering)
Shrinivas Chimmalgi (TU Delft - Mechanical Engineering)
Peter J. Prins (TU Delft - Mechanical Engineering)
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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.
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