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- W4310562148 abstract "The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible to find these Koopman eigenfunctions exactly and analytically. Here, this is done for the Korteweg-de Vries equation on a periodic interval, using the periodic inverse scattering transform and some concepts of algebraic geometry. To the authors' knowledge, this is the first complete Koopman analysis of a partial differential equation which does not have a trivial global attractor. The results are shown to match the frequencies computed by the data-driven method of dynamic mode decomposition (DMD). We demonstrate that in general DMD gives a large number of eigenvalues near the imaginary axis, and show how these should be interpretted in this setting." @default.
- W4310562148 created "2022-12-12" @default.
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- W4310562148 date "2022-11-30" @default.
- W4310562148 modified "2023-09-27" @default.
- W4310562148 title "Koopman analysis of the periodic Korteweg-de Vries equation" @default.
- W4310562148 doi "https://doi.org/10.48550/arxiv.2211.17119" @default.
- W4310562148 hasPublicationYear "2022" @default.
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