Analysis of soliton fission over a submerged structure using "nonlinear Fourier transform (NLFT)"

When a single incident solitary wave passes over a submerged reef, it disintegrates into a train of solitons (soliton fission), followed by a train of oscillatory waves. One of the major problems in the analysis of the recorded time series is the uncertain identification of the number of solitons Nsol in the transmitted wave train behind the reef due to the difficulties to distinguish between solitons and oscillatory waves, especially in the case of breaking waves. With the “nonlinear Fourier transform (NLFT)”, an application of the inverse scattering transform (IST) of the Korteweg-deVries equation, a powerful analysis method is proposed to analyze nonlinear wave processes. The application of the NLFT to the transmitted waves of systematic numerical tests with breaking and non-breaking solitary waves behind a submerged structure (reef) with finite width br allows separating distinctly solitons and oscillatory waves. The presentation gives an overview over the first NLFT analysis results for the determination of the number of solitons N behind the reef. The influence of relative submergence depth dr/h, relative reef width br/Li and relative incident wave height Hi/dr is examined. First recommendations for the distinct identification of the number of solitons rising from the fission using NLFT will also be provided, including the limitations of the method. Finally, first results of the application of the Hilbert-Huang transform (HHT) to the identification of the transmitted solitons are presented.

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