  This study shows that the stability of solitary waves excited in a lipid
monolayer near a phase boundary requires positive curvature of the adiabats, a
known necessary condition in shock compression science. It is further shown
that the condition results in a threshold for excitation, saturation of the
wave amplitude and the splitting of the wave at the phase boundaries. Splitting
in particular confirms that a hydrated lipid interface can undergo condensation
on adiabatic heating thus showing retrograde behavior. Finally, using the new
theoretical insights and state dependence of conduction velocity in nerves, the
curvature of the adiabatic state diagram is shown to be closely tied to the
thermodynamic blockage of nerve pulse propagation.
