Long-time analysis of nonlinearly perturbed wave equations via
modulated Fourier expansions
D. Cohen, E. Hairer and Ch. Lubich
Abstract.
A modulated Fourier expansion in time is used to show
long-time near-conser\-vation of the harmonic actions associated with
spatial Fourier modes
along the solutions of nonlinear wave equations
with small initial data.
The result implies the long-time near-preservation of the
Sobolev-type norm that specifies the
smallness condition on the initial data.
Key Words.
Nonlinear wave equation.