Scaling laws for breathing frequencies of solitary modes in the Zakharov equations.

We analyze typical time scales resulting from the coupled dynamics of high- and low-frequency wave components in solitary solutions of the Zakharov equations. Linear stability analysis around the solitary modes suggests that adiabatic regimes may be obtained in the limit of high- and low-field intensities where the disparity of eigenfrequencies is large. Full simulations, however, reveal that adiabaticity arising from oscillatory motion can in fact be observed only over relatively short periods of time prior to noticeable radiation emission.