PreprintarXiv licencearXiv
Higher-order necessary conditions for nonscattering
Abstract
We study the scattering of incident waves by a class of planar analytic inhomogeneities with constant refractive index, governed by the Helmholtz equation. We derive an infinite hierarchy of necessary conditions for nonscattering: any complex analytic nonscattering incident wave must satisfy infinitely many differential constraints at a specific point determined by the geometry of the inhomogeneity. As an application, we show that for any noncircular elliptical inhomogeneity, every single separated (Mathieu) mode necessarily scatters. This is in stark contrast to the circular case, where single separated (Bessel) modes are nonscattering at infinitely many wavenumbers.
Related
- Ad-conditions for higher-order recurrences: Dunkl and matrix-valued settings
- Local well-posedness of the higher-order nonlinear Schrödinger equation on the half-line: the case of two boundary conditions
- Blowup of smooth solutions to 2D quasilinear wave equations with higher-order null conditions and short pulse initial data
- Higher order KdV-type equations with Robin boundary conditions on ℝ+
- Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion
BibTeX
@misc{hovsepyan2026higherorder,
title = {{Higher-order necessary conditions for nonscattering}},
author = {Narek Hovsepyan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21338},
eprint = {2610.21338},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21338},
}
RIS
TY - UNPB
TI - Higher-order necessary conditions for nonscattering
AU - Narek Hovsepyan
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21338
UR - https://arxiv.org/abs/2610.21338
AB - We study the scattering of incident waves by a class of planar analytic inhomogeneities with constant refractive index, governed by the Helmholtz equation. We derive an infinite hierarchy of necessary conditions for nonscattering: any complex analytic nonscattering incident wave must satisfy infinitely many differential constraints at a specific point determined by the geometry of the inhomogeneity. As an application, we show that for any noncircular elliptical inhomogeneity, every single separated (Mathieu) mode necessarily scatters. This is in stark contrast to the circular case, where single separated (Bessel) modes are nonscattering at infinitely many wavenumbers.
ER -