Small amplitude limit

From DispersiveWiki

The small amplitude limit for a nonlinear equation arises when considering initial position $u (0)$ of the form $u (0) = ε f$ for some fixed $f$ and a small parameter $ε > 0$ , in the limit $\epsilon \to 0$ . For equations which are second-order in time, such as nonlinear wave equations, one must also specify an initial velocity $u t (0) = ε g$ .

For bounded times, the small amplitude limit is usually just the linear counterpart of the equation; however when analyzing long times (e.g. times comparable to $1 / ε$ ), significant nonlinear effects may still occur in the limit.

Retrieved from "http://tosio.math.toronto.edu/wiki/index.php/Small_amplitude_limit"

Category: Limits