Soliton phase shift calculation for the Korteweg–de Vries equation

Peter J. Prins, Sander Wahls
2019 IEEE Access  
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 (NFT), solitons can be detected and characterized before they emerge. In this paper, we present a new algorithm aimed at computing the phase shift of
more » ... hase shift of solitons in processes governed by the Korteweg-de Vries (KdV) equation. In numerical examples, the new algorithm is found to perform reliably even in cases where existing algorithms break down. INDEX TERMS Korteweg-de Vries (KdV) equation, non-linear Fourier transform (NFT), norming constant, soliton, water wave. 122914 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 7, 2019
doi:10.1109/access.2019.2932256 fatcat:uyutj2olf5hdxm6a5xsni6wkxm