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- W2133867530 abstract "The aim of the paper is to discuss the usefulness of the non-linear Schrdif- ferential equation in the study of transformations of progressive deep water waves. Its solution compared with a regular Stokes type wave is essentially restricted to the first order approximation of the second one. The difference is that the Schr¨ equation introduces the concepts of a carrier wave and complex amplitude. In this way the dispersion relation of the third order Stokes expansion is taken into account. The analysis starts with regular, non breaking Stokes waves with large amplitudes as measured in our laboratory. The third order approximation is considered and compared with the corresponding solution of the Schrequation. Then small periodic modifications are introduced in the time series fed into the control system of the generator. The approximation by trigonometric series is applied and the sim- plified analysis of superposition of very small modifications is used (higher powers of modifications are neglected). The Schr¨ odinger non-linear equation is used in this analysis. The comparison of experimental and calculated envelopes is good, but for the surface elevations in space it is not as good. The approximation by trigonometric series is also applied to study the case of larger modifications. Finally the solutions of the Schr¨ odinger equation corresponding to perfect solitons, are compared with the experimental data for cases where the measured surface elevations look almost like periodic solitons. This gives a reasonable approximation of the real behaviour in a very short space interval. It is not easy to get a good numerical description for the wave problem discussed as the waves are physically unstable. The results of the presented research will be used to establish an effective numerical procedure, stress the approximations introduced by the application of the Schrdifferen- tial equation and show how the theoretical solutions should be compared with the measured data." @default.
- W2133867530 created "2016-06-24" @default.
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- W2133867530 date "2005-01-01" @default.
- W2133867530 modified "2023-09-27" @default.
- W2133867530 title "Theoretical analysis on experiments in transformation of deep-water-waves" @default.
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