Envelope quasi-solitons in dissipative systems with cross-diffusion

We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from boundaries and penetrate each other. Presently we demonstrate a different type of quasi-solitons, with a phenomenology resembling that of the envelope solitons in Nonlinear Schroedinger equation: spatiotemporal oscillations with a smooth envelope, with the velocity of the oscillations different from the velocity of the envelope.