Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues

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Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues. / Nazarov, S. A.

In: St. Petersburg Mathematical Journal, Vol. 28, No. 3, 01.01.2017, p. 377-410.

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

BibTeX

@article{1091d90e03764e0b80a2a75e88c83e69,

title = "Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues",

abstract = "The definition and an existence criterion are given for the standing waves at the threshold of the continuous spectrum for a periodic quantum waveguide with a resonator (the Dirichlet problem for the Laplace operator). Such waves and their linear combinations do not transfer energy to infinity, and they only differ from the standing waves with the zero Floquet parameter by an exponentially decaying term. It is shown that the almost standing and trapped waves at the threshold generate eigenvalues in the discrete spectrum of a waveguide with a regular sloping local perturbation of the wall.",

keywords = "Almost standing waves, Asymptotics, Discrete spectrum, Periodic waveguide, Resonator, Threshold scattering matrix",

author = "Nazarov, {S. A.}",

year = "2017",

month = jan,

day = "1",

doi = "10.1090/spmj/1455",

language = "English",

volume = "28",

pages = "377--410",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "3",

}

RIS

TY - JOUR

T1 - Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues

AU - Nazarov, S. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The definition and an existence criterion are given for the standing waves at the threshold of the continuous spectrum for a periodic quantum waveguide with a resonator (the Dirichlet problem for the Laplace operator). Such waves and their linear combinations do not transfer energy to infinity, and they only differ from the standing waves with the zero Floquet parameter by an exponentially decaying term. It is shown that the almost standing and trapped waves at the threshold generate eigenvalues in the discrete spectrum of a waveguide with a regular sloping local perturbation of the wall.

AB - The definition and an existence criterion are given for the standing waves at the threshold of the continuous spectrum for a periodic quantum waveguide with a resonator (the Dirichlet problem for the Laplace operator). Such waves and their linear combinations do not transfer energy to infinity, and they only differ from the standing waves with the zero Floquet parameter by an exponentially decaying term. It is shown that the almost standing and trapped waves at the threshold generate eigenvalues in the discrete spectrum of a waveguide with a regular sloping local perturbation of the wall.

KW - Almost standing waves

KW - Asymptotics

KW - Discrete spectrum

KW - Periodic waveguide

KW - Resonator

KW - Threshold scattering matrix

UR - http://www.scopus.com/inward/record.url?scp=85017102561&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=29500577

U2 - 10.1090/spmj/1455

DO - 10.1090/spmj/1455

M3 - Article

AN - SCOPUS:85017102561

VL - 28

SP - 377

EP - 410

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 3

ER -

ID: 40974152