Oscillatory pulse - Knowlpedia

An oscillatory pulse is a field of the form

w(v,x)=\chi(v)a(v,x)e^{i\kappa\Phi(v,x)},

where a cutoff or decay of the amplitude localizes it in the pulse coordinate $v$ . The phase produces rapid oscillations; a pulse envelope describes the amplitude's growth and decay. Additional spatial cutoffs can localize the pulse in space.

Effect of localization

Multiplying a solution amplitude by $\chi$ creates a term $\chi'a$ in a first-order evolution equation. It is small only if one has bounds for the amplitude where $\chi'\ne0$ . Exponential smallness near pulse endpoints can control this error; localization alone does not preserve an exact equation.