The conventional Fourier transform (FT) is the most common analysis method in the frequency domain. The measured signal is decomposed into sine and cosine waves as linear basic components. Every basic component is represented in the Fourier spectrum by its wave amplitude, frequency and phase. As an extension to the conventional FT, this paper presents the advanced “nonlinear Fourier transform (NLFT)” as an alternative nonlinear approach for the analysis of nonlinear shallow water waves. The NLFT uses nonlinear cnoidal waves as basic components and considers their nonlinear wave-wave interactions in the analysis. The application of the NLFT to the analysis of numerical test data is shown using examples of soliton fission over and behind submerged reefs. The determined nonlinear Fourier spectra illustrate the capability of this method and its advantages as compared to the conventional FT.

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