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Journal article
Conservative integrators for a toy model of weak turbulence
Journal of computational and applied mathematics, v 325, pp 113-124
01 Dec 2017
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Abstract
Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourgain that the 2D defocusing nonlinear Schrodinger equation (NLS) on the torus has this dynamic, and several analytical and numerical studies have worked towards addressing this point.
In the process of studying the conjecture, Colliander, Keel, Staffilani, Takaoka, and Tao introduced a "toy model" dynamical system as an approximation of NLS, which has been subsequently studied numerically. In this work, we formulate and examine several numerical schemes for integrating this model equation. The model has two invariants, and our schemes aim to conserve at least one of them. We prove convergence in some cases, and our numerical studies show that the schemes compare favorably to others, such as Trapezoidal Rule and fixed step fourth order Runge Kutta. The preservation of the invariants is particularly important in the study of weak turbulence as the energy transfer tends to occur on long time scales. (C) 2017 Elsevier B.V. All rights reserved.
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Details
- Title
- Conservative integrators for a toy model of weak turbulence
- Creators
- Aquil D. Jones - Drexel UniversityGideon Simpson - Drexel UniversityWilliam Wilson - Drexel University
- Publication Details
- Journal of computational and applied mathematics, v 325, pp 113-124
- Publisher
- Elsevier
- Number of pages
- 12
- Grant note
- DMS-1409018 / US National Science Foundation; National Science Foundation (NSF) 1409018 / Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000404308000008
- Scopus ID
- 2-s2.0-85019833311
- Other Identifier
- 991019168663004721
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- Web of Science research areas
- Mathematics, Applied