Abstract
AbstractWe study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by 2n measurements up to a natural gauge. We also show that one can recover the full first-order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and Salo (SIAM J Math Anal 52(6):5467–5499, 2020) and (Inverse Probl 36(3):035005, 2020) to Hamiltonians with first-order perturbations, and it is based on wave equation methods and Carleman estimates.
Funder
Ministerio de Economía y Competitividad
Academy of Finland
H2020 European Research Council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference27 articles.
1. Barceló, J.A., Castro, C., Luque, T., Meroño, C.J., Ruiz, A., Vilela, M.C.: Uniqueness for the inverse fixed angle scattering problem. J. Inverse Ill-Posed Probl. 28(4), 465–470 (2020)
2. Bayliss, A., Li, Y., Morawetz, C.: Scattering by a potential using hyperbolic methods. Math. Comput. 52(186), 321–338 (1989)
3. Bellassoued, M., Yamamoto, M.: Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems. Springer Monographs in Mathematics. Springer (2017)
4. Bukhgeim, A., Klibanov, M.: Global uniqueness of class of multidimensional inverse problems. Soviet Math. Dokl. 24, 244–247 (1981)
5. Cristofol, M., Soccorsi, E.: Stability estimate in an inverse problem for non-autonomous Schrödinger equations. Appl. Anal. 90(10), 1499–1520 (2011)
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