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Dubrovin equation for periodic Dirac operator on the half-line. / Korotyaev, Evgeny; Mokeev, Dmitrii.

в: Applicable Analysis, Том 101, № 1, 20.03.2020, стр. 337-365.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Korotyaev, E & Mokeev, D 2020, 'Dubrovin equation for periodic Dirac operator on the half-line', Applicable Analysis, Том. 101, № 1, стр. 337-365. https://doi.org/10.1080/00036811.2020.1742882

APA

Korotyaev, E., & Mokeev, D. (2020). Dubrovin equation for periodic Dirac operator on the half-line. Applicable Analysis, 101(1), 337-365. https://doi.org/10.1080/00036811.2020.1742882

Vancouver

Korotyaev E, Mokeev D. Dubrovin equation for periodic Dirac operator on the half-line. Applicable Analysis. 2020 Март 20;101(1):337-365. https://doi.org/10.1080/00036811.2020.1742882

Author

Korotyaev, Evgeny ; Mokeev, Dmitrii. / Dubrovin equation for periodic Dirac operator on the half-line. в: Applicable Analysis. 2020 ; Том 101, № 1. стр. 337-365.

BibTeX

@article{f01e1eef639c4cc6839546b54ffd0dbd,
title = "Dubrovin equation for periodic Dirac operator on the half-line",
abstract = "We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface with a unique simple pole on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called levels and there are no other poles. If the potential is shifted by real parameter t, then the continuous spectrum does not change but the levels can change their positions. We prove that each level is smooth and in general, non-monotonic function of t. We prove that a level is a strictly monotone function of t for a specific potential. Using these results, we obtain formulas to recover potentials of special forms.",
keywords = "Dirichlet eigenvalues, Dubrovin equation, Periodic Dirac operator, resonances, SCHRODINGER OPERATOR, INVERSE PROBLEM",
author = "Evgeny Korotyaev and Dmitrii Mokeev",
note = "Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2020",
month = mar,
day = "20",
doi = "10.1080/00036811.2020.1742882",
language = "English",
volume = "101",
pages = "337--365",
journal = "Applicable Analysis",
issn = "0003-6811",
publisher = "Taylor & Francis",
number = "1",

}

RIS

TY - JOUR

T1 - Dubrovin equation for periodic Dirac operator on the half-line

AU - Korotyaev, Evgeny

AU - Mokeev, Dmitrii

N1 - Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2020/3/20

Y1 - 2020/3/20

N2 - We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface with a unique simple pole on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called levels and there are no other poles. If the potential is shifted by real parameter t, then the continuous spectrum does not change but the levels can change their positions. We prove that each level is smooth and in general, non-monotonic function of t. We prove that a level is a strictly monotone function of t for a specific potential. Using these results, we obtain formulas to recover potentials of special forms.

AB - We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface with a unique simple pole on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called levels and there are no other poles. If the potential is shifted by real parameter t, then the continuous spectrum does not change but the levels can change their positions. We prove that each level is smooth and in general, non-monotonic function of t. We prove that a level is a strictly monotone function of t for a specific potential. Using these results, we obtain formulas to recover potentials of special forms.

KW - Dirichlet eigenvalues

KW - Dubrovin equation

KW - Periodic Dirac operator

KW - resonances

KW - SCHRODINGER OPERATOR

KW - INVERSE PROBLEM

UR - http://www.scopus.com/inward/record.url?scp=85082432530&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/15f5dfd5-02e3-3afa-8c8b-60fbaaa78151/

U2 - 10.1080/00036811.2020.1742882

DO - 10.1080/00036811.2020.1742882

M3 - Article

AN - SCOPUS:85082432530

VL - 101

SP - 337

EP - 365

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 1

ER -

ID: 52828027