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Metastable energy strata in numerical discretizations ofweakly nonlinear wave equations

Gauckler, Ludwig; Weiß, Daniel

Abstract:
The quadratic nonlinear wave equation on a one-dimensional torus with small initial values located in a single Fourier mode is considered. In this situation, the formation of metastable energy strata has recently been described and their long-time stability has been shown. The topic of the present paper is the correct reproduction of these metastable energy strata by a numerical method. For symplectic trigonometric integrators applied to the equation, it is shown that these energy strata are reproduced even on long time intervals in a qualitatively correct way.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000055097
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-550978
KITopen ID: 1000055097
Verlag KIT, Karlsruhe
Umfang 23 S.
Serie CRC 1173 ; 2016/13
Schlagworte nonlinear wave equations, trigonometric integrators, long-time behavior, modulated Fourier expansion
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