Soliton and half-soliton interaction of solitary waves in excitable media with non-linear cross-diffusion

We have studied properties of non-linear waves in a mathematical model of a predator–prey system with taxis. We demonstrate that, for systems with negative and positive taxis there typically exists a large region in the parameter space, where the waves demonstrate quasi-soliton interaction; colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries. In this paper, we use numerical simulations to demonstrate also a new wave phenomenon — a half-soliton interaction of waves, when of two colliding waves, one annihilates and the other continues to propagate. We show that this effect depends on the “ages” or, equivalently, “widths” of the colliding waves.