Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity

.We study the nondiffusive Westervelt equation in the weakly nonlinear regime and show that the leading profile equation is of Burgers' type. We show that a compactly supported nonlinearity coefficient \(\alpha\) can be reconstructed from the tilt of the transmitted high frequency wave packets sent from different directions, by demonstrating that those tilts are proportional to the X-ray transform of \(\alpha\).KeywordsWesterveltnonlinear opticsgeometric opticsinverse problemMSC codes35R30