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

Classification of wave regimes in excitable systems with linear cross-diffusion