an:04055152
Zbl 0646.73016
Chierchia, L.; Ercolani, N.; McLaughlin, D.
On the weak limit of rapidly oscillating waves
EN
Duke Math. J. 55, 759-764 (1987).
00152665
1987
j
74J99 35Q99 74J20
averaging theorem; locally non-resonant curves
A possible representation of a rapidly oscillating wave can be represented as
\[
U^{\epsilon}(x,t)=W_ N(\theta (x,t)/\epsilon;\quad \kappa (x,t),\quad \omega (x,t))+O(\epsilon),
\]
where \(W_ N(\cdot,\kappa,\omega):T^ N\to R\) is defined on the N-torus \(T^ N\) and the N-vectors \(\theta\), \(\kappa\), \(\omega\) are real-valued functions of x and t related by \((\partial \theta /\partial x)=\kappa\), \((\partial \theta /\partial t)=\omega\). An averaging theorem is proved on the so- called locally non-resonant curves \(\kappa:R\to R^ n.\)
V.R??svan
Zbl 0605.35079