  We consider principal properties of various wave regimes in two selected
excitable systems with linear cross-diffusion in one spatial dimension observed
at different parameter values. This includes fixed-shape propagating waves,
envelope waves, multi-envelope waves, and intermediate regimes appearing as
waves propagating fixed-shape most of the time but undergoing restructuring
from time to time. Depending on parameters, most of these regimes can be with
and without the "quasi-soliton" property of reflection of boundaries and
penetration through each other. We also present some examples of behaviour of
envelope quasi-solitons in two spatial dimensions.
