The application of the KdV type equation in engineering simulation

Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations and later discrete solitons are strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the initial mean bore height. The complete disintegration of the initial bore into a train of solitons requires very long propagation, but unfortunately, these required distances are usually not available in experimental tests of nature. Therefore, the analysis of the bore decomposition for experimental data into solitons is complicated and requires different approaches. Previous studies have shown that by applying the nonlinear Fourier transform based on the Ko- rteweg–de Vries equation (KdV-NFT) to bores and long-period waves propagating in constant depth, the number and height of all solitons can be reliably predicted already based on the initial bore-shaped free surface. Against this background, this study presents the systematic analysis of the leading-soliton amplitudes for non-breaking and breaking bores with different strengths in different water depths to validate the KdV-NFT results for non-breaking bores to show the limitations of wave breaking on the spectral results. The analytical results are compared with data from experimental tests, numerical simulations and other approaches from the literature.

Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

A minimum mean squared error (MMSE) equalizer is a way to effectively increase transmission performance for nonlinear Fourier transform (NFT) based communication systems. Other equalization schemes, based on nonlinear equalizer approaches or neural networks, are interesting for NFT transmission due to their ability to deal with nonlinear correlations of the NFTs’ eigenvalues and their coefficients. We experimentally investigated single- and dual-polarization long haul transmission with several modulation schemes and compared different equalization techniques including joint detection equalization and the use of neural networks. We observed that joint detection equalization provides range increases for shorter transmission distances while having low numeric complexity. We could further achieve bit error rates (BER) under HD-FEC for significant longer transmission distances in comparison to no equalization with different equalizers.<div><br></div><div>Manuscript received August 6, 2020; revised November 2, 2020; accepted December 8, 2020. Date of publication December 16, 2020;<br></div>