Stability of solitary waves in membrane tubes: A weakly nonlinear analysis

We study the problem of the stability of solitary waves propagating in fluid-filled membrane tubes. We consider only waves whose speeds are close to speeds satisfying a linear dispersion relation (it is well known that there can be four families of solitary waves with such speeds), i.e., the waves with small (but finite) amplitudes branching from the rest state of the system. In other words, we use a weakly nonlinear description of solitary waves and show that if the solitary wave speed is bounded from zero, then the solitary wave itself is orbitally stable independently of whether the fluid is in the rest state at the initial time.