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- W2060847477 abstract "We demonstrate that the stationary solutions of the nonlinear Schrödinger equation (NLS) give rise to families of orthonormal bases for the square integrable functions with periodic boundary conditions. This allows us to use these solutions in the same way as regular Fourier modes or other basis sets. For instance, we show the applicability of the NLS basis sets for doing data analysis, and as a means for obtaining reduced models. Using a variety of examples, we show that working with the NLS basis sets is advantageous over working with the set of Fourier modes, which they contain as a special case. The NLS sets are particularly appealing for those problems where the NLS equation is expected to provide a good description of any underlying dynamics, such as the description of modulated waves in deep water or nonlinear optics. In those cases, the decomposition of experimental data requires fewer modes compared to regular Fourier analysis, and the truncated components remain unimportant on longer time scales." @default.
- W2060847477 created "2016-06-24" @default.
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- W2060847477 date "2010-04-01" @default.
- W2060847477 modified "2023-10-17" @default.
- W2060847477 title "Data analysis and reduction using stationary solutions of the NLS equation" @default.
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- W2060847477 doi "https://doi.org/10.1080/00036810903569481" @default.
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