Reliable numerical algorithms for the Non-linear Fourier Transform of the KdV equation

<b>Research question</b><br/>The topic of this dissertation is the numerical computation of the forward and inverse Non-linear Fourier Transform (NFT) for the Korteweg–de Vries equation (KdV), for sampled signals that decay sufficiently fast on both sides. With NFTs certain non-linear Partial Differential Equations (PDEs) can be solved in a way...

Soliton phase shift calculation for the Korteweg–de Vries equation

Several non-linear fluid mechanical processes, such as wave propagation in shallow water, are known to generate solitons: localized waves of translation. Solitons are often hidden in a wave packet at the beginning and only reveal themselves in the far-field. With a special signal processing technique known as the non-linear Fourier transform ...