Metastable energy strata in numerical discretizations of weakly nonlinear wave equations. (English) Zbl 1360.65299
Summary: 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.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65P40 | Numerical nonlinear stabilities in dynamical systems |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35L05 | Wave equation |
Keywords:
nonlinear wave equation; trigonometric integrators; symplectic integrators; long-time behaviour; modulated Fourier expansionReferences:
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