Skip Navigation

The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(1):107-137; doi:10.1093/qjmam/54.1.107
© 2001 by Oxford University Press
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (8)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Shanin, A. V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Three theorems concerning diffraction by a strip or a slit

Andrey V. Shanin1,+

( 1 Department of Physics, Acoustics, Moscow State University, Leninskie Gory, Moscow 119899, Russia )

The problem of diffraction on a strip or a slit is under consideration. A functional equation of Wiener–Hopf type is derived; analytical restrictions are imposed on unknown functions. The solution of a functional problem (the spectrum of the scattered field) is proved to be a solution of an ordinary differential equation with rational coefficients known up to several numerical constants. A nonlinear differential equation describing the dependence of unknown constants on the width of the strip (slit) is derived. Connection between the methods developed here and the solution in the form of Schwarzschild series is established.

Received 3 May, 1999. Revised 5 May, 2000.

+ (shanin@ort.ru)


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Q J Mechanics Appl MathHome page
J. Bernard
A spectral approach for scattering by impedance polygons
Q J Mechanics Appl Math, November 1, 2006; 59(4): 517 - 550.
[Abstract] [Full Text] [PDF]


Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.