Details
| Original language | English |
|---|---|
| Pages (from-to) | 801-819 |
| Number of pages | 19 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 56 |
| Issue number | 1 |
| Early online date | 16 Jan 2024 |
| Publication status | Published - 2024 |
Abstract
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 α 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 α.
Keywords
- geometric optics, inverse problem, nonlinear optics, Westervelt
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 56, No. 1, 2024, p. 801-819.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity
AU - Eptaminitakis, Nikolas
AU - Stefanov, Plamen
N1 - Funding Information: The work of the second author was partially supported by NSF grant DMS-2154489. \dagger Institut fu\"r Differentialgeometrie, Leibniz Universita\"t Hannover, 30167 Hannover, Germany (nikolaos.eptaminitakis@math.uni-hannover.de). \ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA (stefanov@math. purdue.edu).
PY - 2024
Y1 - 2024
N2 - 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 α 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 α.
AB - 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 α 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 α.
KW - geometric optics
KW - inverse problem
KW - nonlinear optics
KW - Westervelt
UR - http://www.scopus.com/inward/record.url?scp=85183722861&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2208.13945
DO - 10.48550/arXiv.2208.13945
M3 - Article
AN - SCOPUS:85183722861
VL - 56
SP - 801
EP - 819
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 1
ER -