Trapping of energy into solitary waves in amplified nonlinear dispersive systems

A number of examples have recently been found in which stable, highly compressed pulses are produced in fibers on much shorter length scales than those present initially. These systems involve energy flow among different nonlinear waves. We present numerical model calculations that exhibit this compression when energy is pumped into the nonlinear wave. These models are simple enough to provide some understanding of the underlying generic behavior. We also present a theory of these results that relates thr length scale of the pulse to the evolution of the energy.