Inverse Scattering for Waveguides

Isozaki, Hiroshi; Kurylev, Yaroslav; Lassas, Matti

doi:10.5802/tsg.248

Isozaki, Hiroshi ¹ ; Kurylev, Yaroslav ² ; Lassas, Matti 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, Tome 25 (2006-2007), pp. 71-83.

Résumé

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

Affiliations des auteurs :

Isozaki, Hiroshi ¹ ; Kurylev, Yaroslav ² ; Lassas, Matti ³

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     author = {Isozaki, Hiroshi and Kurylev, Yaroslav and Lassas, Matti},
     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},
     doi = {10.5802/tsg.248},
     mrnumber = {2478809},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/tsg.248/}
}

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Isozaki, Hiroshi; Kurylev, Yaroslav; Lassas, Matti. Inverse Scattering for Waveguides. Séminaire de théorie spectrale et géométrie, Tome 25 (2006-2007), pp. 71-83. doi : 10.5802/tsg.248. http://www.numdam.org/articles/10.5802/tsg.248/

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