Dynamical stability of running solitary waves in fluid-filled elastic membrane tubes

We examine the problem of stability of solitary waves, propagating in a fluid-filled membrane tube. We consider waves with speeds starting from those given by the linear dispersion relation (it is known that there may exist four families of solitary waves having such speeds), i. e. the waves of a finite amplitude bifurcating from the quiescent state of the system. It is shown that if a solitary wave speed is bounded away from zero the solitary wave itself is orbitally stable, when the fluid initially stationary (the mean flow is absent).