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math.AP2026
Plane-wave representation for the Laplace--Beltrami equation on a sphere. Application to the Green's function
Andrey V. Shanin, Valentin D. Kunz, Raphael C. Assier
We propose an extension of the plane-wave representation for wave fields defined on the real sphere . This representation is well-known in the planar setting but has…
math.AP2025
Asymptotic evaluation of three-dimensional integrals with singularities in application to wave phenomena
A. V. Shanin, A. Yu. Laptev
We consider a three-dimensional Fourier integral in which the exponent in the exponential factor is the product of some phase function and a large parameter. The asymptotics of thi…
math.AP2024
A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
Andrey V. Shanin, Raphael C. Assier, Andrey I. Korolkov +1
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integr…