The formation of shocks in waves of advance in nonlinear partial differential equations is a well-explored problem and has been studied using many different techniques. In this paper we demonstrate how an exponential-asymptotic approach can be used to characterise completely the shock formation in a nonlinear PDE and so resolve an apparent paradox concerning the asymptotic modelling of shock formation. In so doing, we find that the recently discovered higher-order Stokes phenomenon plays a significant, previously unrealised, role in the asymptotic analysis of shocks. For the purposes of clarity, Burgers’ equation is used as a pedagogical example, but the techniques illustrated are more generally applicable
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.