Metastable Energy Strata in Numerical Discretizations of Weakly Nonlinear Wave Equations
Discrete and continuous dynamical systems(2017)
摘要
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.
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关键词
Nonlinear wave equation,trigonometric integrators,symplectic integrators,long-time behaviour,modulated Fourier expansion
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