Sommerfeld Malyuzhinets (SM) method and the Wiener Hopf (WH) technique are

different but c losely related methods. In particular in the paper &ldquo\;Progress and

Prospects in The Theory o f Linear Waves Propagation&rdquo\; SIAM SIREV vol. 21\, No.2\,

April 1979\, pp. 229-245\, J.B. Kel ler posed the following question &ldquo\;What

f eatures of the methods account for this difference ?&rdquo\;. Furthermore

J.B. Keller notes &ldquo \;it might be

helpful to understand this in ord er to predict the success of other methods&rdquo\; .

We

agree with this opinion expressed b y the giant of Diffraction. Furthermore we think t hat SM and

WH applied to the same problems (for instance the polygon diffraction) can determine a helpful synergy. In the past

the SM and WH met hods were considered disconnected in particular be cause the SM

method was traditionally defined w ith the angular complex representation while

th e WH method was traditionally defined in the Lapla ce domain.

In

this course we show that t he two methods have significant points of similari ty

when the representation of problems in both methods are expressed in terms of

difference eq uations. The two methods show their diversity in t he solution

procedures that are completely diff erent and effective.

Both similarity and divers ity properties are of advantage in &ldquo\;Progres s and Prospects in The Theory of

Linear Waves P ropagation&rdquo\;. Moreover

both methods have demonstrated their efficacy in studying particular ly complex

problems\, beyond the traditional pr oblem of scattering by a wedge: in

particular t he scattering by a three part polygon that we will present.

Recent

progress in both metho ds:

One

of the most relevant recent prog ress in SM is the derivation of functional

diff erence equations without the use of Maliuzhinets i nversion theorem.

One

of the most relevant recent progress in WH is transformation of WH equa tions

into integral equations for their effecti ve solution. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR