  The paper deals with the studies of the nonlinear wave solutions supported by
the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work
that the model, under certain conditions, possesses a set of soliton-like
traveling wave (TW) solutions. In this paper we show that the model has two
solutions of the soliton type differing in propagation velocity. Their location
in parametric space, and stability properties are considered in more details.
Numerical results accompanied by the application of the Evans function
technique prove the stability of fast solitary waves and instability of slow
ones. A possible way of formation and annihilation of localized regimes in
question is studied therein too.
