Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method-Reference-Cited by-同舟云学术

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

Published:2024-03-13 Issue:2 Volume:5 Page:
ISSN:2662-2963
Container-title:Partial Differential Equations and Applications
language:en
Short-container-title:Partial Differ. Equ. Appl.

Author:

Kalimeris Konstantinos^ORCID,Mindrinos Leonidas^ORCID

Abstract

AbstractWe 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.

Funder

Research Committee, Academy of Athens

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s42985-024-00277-z.pdf

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