Pulse interactions in an unstable dissipative-dispersive nonlinear system

Abstract

An attempt is made to understand several features of the wave evolutions in an unstable dissipative-dispersive nonlinear system in terms of the interactions of localized solitonlike pulses. It is found that the wave evolutions can be qualitatively well described by weak interactions of pulses, each of which is the steady solution to the original evolution equation. The oscillatory structure of a tail of the pulse for weakly dispersive cases is responsible for the existence of bound states of pulses, which explains the numerical result that the interpulse distances in the initial value problem take certain fixed values or values in the definite regions. In cases of monotone tails for strongly dispersive cases, the effects of pulse interactions become repulsive, which explains the result that the pulses asymptotically tend to be arranged periodically, adjusting to the periodic boundary conditions in the numerical simulation.