Inverse Scattering for Waveguides

Hiroshi Isozaki; Yaroslav Kurylev; Matti Lassas

doi:10.5802/tsg.248

Hiroshi Isozaki ¹; Yaroslav Kurylev ²; Matti Lassas ³

¹ University of Tsukuba Institute of Mathematics Tsukuba, 305-8571 (Japan)
² University College of London Department of Mathematics United Kingdom
³ Helsinki University of Technology Department of Mathematics Finland

Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 71-83.

Abstract

We study the inverse scattering problem for a waveguide $(M, g)$ with cylindrical ends, $M = M^{c} \cup (\cup_{α = 1}^{N} (Ω^{α} \times (0, \infty)))$ , where each $Ω^{α} \times (0, \infty)$ has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines $(M, g)$ up to an isometry.

DOI: 10.5802/tsg.248

Classification: 58J50, 35R30

Author's affiliations:

Hiroshi Isozaki ¹; Yaroslav Kurylev ²; Matti Lassas ³

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     title = {Inverse {Scattering} for {Waveguides}},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {71--83},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     year = {2006-2007},
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     mrnumber = {2478809},
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     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.248/}
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Hiroshi Isozaki; Yaroslav Kurylev; Matti Lassas. Inverse Scattering for Waveguides. Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 71-83. doi : 10.5802/tsg.248. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.248/

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