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

2022/08/30 by Nikolas Eptaminitakis, Plamen Stefanov, Eptaminitakis, Nikolas +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2208.13945

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 α 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 α.

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