Journal article
Born and inverse Born series for scattering problems with Kerr nonlinearities
INVERSE PROBLEMS, v 39(12), 125015
01 Dec 2023
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments.
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Details
- Title
- Born and inverse Born series for scattering problems with Kerr nonlinearities
- Publication Details
- INVERSE PROBLEMS, v 39(12), 125015
- Publisher
- IOP Publishing Ltd; BRISTOL
- Grant note
- We are indebted to Jonah Blasiak and R Andrew Hicks for their assistance with the proof of lemma 3. This work was carried out when N DeFelippis was a member of the Department of Mathematics at Drexel University. S Moskow and N DeFelippis were supported by the NSF Grant DMS-2008441. J Schotland was supported by the NSF Grant DMS-1912821 and the AFOSR Grant FA9550-19-1-0320.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:001096019900001
- Scopus ID
- 2-s2.0-85177496243
- Other Identifier
- 991021861209904721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical