Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method

Konstantinos Kalimeris () and Leonidas Mindrinos ()
Additional contact information
Konstantinos Kalimeris: Academy of Athens
Leonidas Mindrinos: Agricultural University of Athens

Partial Differential Equations and Applications, 2024, vol. 5, issue 2, 1-25

Abstract: Abstract We derive the extension of the classical d’Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index. Analogous formulae exist already in the literature, but in the current work this is derived in a natural way for general incident field, by employing results obtained via the Fokas method. This methodology is further extended to a medium with piecewise constant refractive index, providing the apparatus for the solution of the associated inverse scattering problem. Hence, we provide an exact reconstruction method which is also valid for phaseless data.

Keywords: Wave equation; D’Alembert formula; Fokas method; Inverse scattering; Reconstruction; 35L05; 35A22; 35R30; 35S30 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-024-00277-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:5:y:2024:i:2:d:10.1007_s42985-024-00277-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-024-00277-z

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().