Soliton Phase Shift Calculation for the Korteweg–De Vries Equation

Abstract

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 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.

Keywords

• Korteweg–de Vries (KdV) equation
• non-linear Fourier transform (NFT)
• norming constant
• soliton
• water wave