Long-Time Analysis of Nonlinearly Perturbed Wave Equations Via Modulated Fourier Expansions

Journal article, 2008

A modulated Fourier expansion in time is used to show long-time near- conservation 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.