Waves, oscillatory double integrals, and multidimensional complex analysis

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• Raphael Assier (University of Manchester)
• Monday 01 July 2024, 14:00-14:30
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

In this talk, I will give an overview of recent developments linking wave theory and multidimensional complex analysis. I will explain how a procedure of complex deformation of the integration surface of Fourier-like highly oscillatory double integrals can lead to closed-form far-field asymptotics results in wave diffraction theory. Each far-field component will be shown to be connected to a special point on the singularity set of the integrand. The procedure will be illustrated through two examples that can be reformulated as two-complex-variables scalar Wiener-Hopf problems: the three-dimensional problem of plane wave diffraction by a quarter-plane and the two-dimensional problem of plane wave diffraction by a penetrable wedge. I will also show how it can be used to shed some light on wave propagation in periodic structures. The talk will cover aspects of several articles written jointly with great collaborators who should be acknowledged: Andrey V. Shanin, Andrey K. Korolkov, Valentin D. Kunz and I. David Abrahams.

This talk is part of the Isaac Newton Institute Seminar Series series.

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