  An axially stretched soft cylindrical tube may develop an infinite-wavelength
instability when one or both of its lateral surfaces are under sufficient
surface tension. For fixed surface tension and increasing axial stretch, this
instability occurs when the resultant axial force attains a maximum, though for
fixed axial stretch and increasing surface tension, no such interpretation
exists. A weakly non-linear analysis is conducted for a general material model
to determine the explicit nature of this instability for multiple loading
scenarios. The bifurcation solution is found to be localised bulging or necking
depending on whether the axial stretch is greater or less than a certain
threshold value at the point of bifurcation. At this threshold value, an
exceptionally super-critical kink wave solution arises in place of
localisation. By drawing upon previous Finite Element Method (FEM) simulations,
and experimental findings for the analogous problem of tubes under internal
inflation, a thorough interpretation of the anticipated post-bifurcation
behaviour is given with the view to aiding future experimental studies of the
problem at hand.
