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arXiv · 1502.04310

Parametric Reduced Models for the Nonlinear Schr\"odinger Equation

John Harlim·Xiantao Li
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Abstract

Reduced models for the (defocusing) nonlinear Schr\"odinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parameterization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

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BibTeXRIS

John Harlim, Xiantao Li. 2015-02-15. Parametric Reduced Models for the Nonlinear Schr\"odinger Equation. https://doi.org/10.1103/physreve.91.053306

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