  In the context of forecasting temperature and pressure fields in
high-intensity focussed ultrasound, the accuracy of predictive models is
critical for the safety and efficacy of treatment. In such fields inertial
cavitation is often observed. Classically, estimations of cavitation thresholds
have been based on the assumption that the incident wave at the surface of a
bubble was the same as in the far-field, neglecting the effect of nonlinear
wave propagation. By modelling the incident wave as a solution to Burgers'
equation using weak shock theory, the effects of nonlinear wave propagation on
inertial cavitation are investigated using both numerical and analytical
techniques. From radius-time curves for a single bubble, it is observed that
there is a reduction in the maximum size of a bubble undergoing inertial
cavitation and that the inertial collapse occurs earlier in contrast with the
classical case. Corresponding stability thresholds for a bubble whose initial
radius is slightly below the critical Blake radius are calculated. Bifurcation
diagrams and frequency-response curves are presented associated with the loss
of stability. The consequences and physical implications of the results are
discussed with respect to the classical results.
