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Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity (2208.13945v1)
Published 30 Aug 2022 in math.AP
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 $\alpha$.
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