Absolute and convective instabilities of waves on unbounded and large bounded domains

Instabilities of nonlinear waves on unbounded domains manifest themselves in different ways. An absolute instability occurs if the amplitude of localized wave packets grows in time at each fixed point in the domain. In contrast, convective instabilities are characterized by the fact that even though the overall norm of wave packets grows in time, perturbations decay locally at each given point in the unbounded domain: wave packets are convected...