Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity

Abstract

We study the non-diffusive Westervelt equation in the weakly nonlinear regime. We show that the leading profile equation is of Burgers' type. We show that a compactly supported nonlinearity $\alpha$ can be reconstructed from the tilt of the transmitted high frequency wave packets sent from different directions since those tilts are proportional to the X-ray transform of $\alpha$.