Mathematical Scattering Theory in Quantum and Acoustic Waveguides

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Mathematical Scattering Theory in Quantum and Acoustic Waveguides. / Plamenevskii, B. A.; Poretskii, A. S.; Sarafanov, O. V.

In: Journal of Mathematical Sciences (United States), Vol. 262, No. 3, 05.05.2022, p. 329-357.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ff641ce80be948abb9a6b61be14dbef2,

title = "Mathematical Scattering Theory in Quantum and Acoustic Waveguides",

abstract = "We consider a waveguide that occupies a domain G with several cylindrical ends and is descried by the nonstationary equation [InlineMediaObject not available: see fulltext.] where [InlineMediaObject not available: see fulltext.] is a selfadjoint second order elliptic operator with variable coefficients. For the boundary condition we consider the Dirichlet, Neumann, or Robin ones. For the stationary problem with parameter we describe eigenfunctions of the continuous spectrum and a scattering matrix. Based on the limiting absorption principle, we obtain an expansion in eigenfunctions of the continuous spectrum. We compute wave operators and prove their completeness. We define a scattering operator and describe its connection with the scattering matrix. As a consequence, we construct scattering theory for the wave equation [InlineMediaObject not available: see fulltext.].",

author = "Plamenevskii, {B. A.} and Poretskii, {A. S.} and Sarafanov, {O. V.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = may,

day = "5",

doi = "10.1007/s10958-022-05820-0",

language = "English",

volume = "262",

pages = "329--357",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Mathematical Scattering Theory in Quantum and Acoustic Waveguides

AU - Plamenevskii, B. A.

AU - Poretskii, A. S.

AU - Sarafanov, O. V.

PY - 2022/5/5

Y1 - 2022/5/5

N2 - We consider a waveguide that occupies a domain G with several cylindrical ends and is descried by the nonstationary equation [InlineMediaObject not available: see fulltext.] where [InlineMediaObject not available: see fulltext.] is a selfadjoint second order elliptic operator with variable coefficients. For the boundary condition we consider the Dirichlet, Neumann, or Robin ones. For the stationary problem with parameter we describe eigenfunctions of the continuous spectrum and a scattering matrix. Based on the limiting absorption principle, we obtain an expansion in eigenfunctions of the continuous spectrum. We compute wave operators and prove their completeness. We define a scattering operator and describe its connection with the scattering matrix. As a consequence, we construct scattering theory for the wave equation [InlineMediaObject not available: see fulltext.].

AB - We consider a waveguide that occupies a domain G with several cylindrical ends and is descried by the nonstationary equation [InlineMediaObject not available: see fulltext.] where [InlineMediaObject not available: see fulltext.] is a selfadjoint second order elliptic operator with variable coefficients. For the boundary condition we consider the Dirichlet, Neumann, or Robin ones. For the stationary problem with parameter we describe eigenfunctions of the continuous spectrum and a scattering matrix. Based on the limiting absorption principle, we obtain an expansion in eigenfunctions of the continuous spectrum. We compute wave operators and prove their completeness. We define a scattering operator and describe its connection with the scattering matrix. As a consequence, we construct scattering theory for the wave equation [InlineMediaObject not available: see fulltext.].

UR - http://www.scopus.com/inward/record.url?scp=85129241769&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/138c307e-d9fb-35a3-8e0f-0f1c59d25aa6/

U2 - 10.1007/s10958-022-05820-0

DO - 10.1007/s10958-022-05820-0

M3 - Article

AN - SCOPUS:85129241769

VL - 262

SP - 329

EP - 357

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 100852292