On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021134" target="_blank" >RIV/62690094:18470/23:50021134 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1134/S0012266123020118" target="_blank" >https://link.springer.com/article/10.1134/S0012266123020118</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S0012266123020118" target="_blank" >10.1134/S0012266123020118</a>
Alternative languages
Result language
angličtina
Original language name
On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity
Original language description
We consider the Schrodinger operator on the plane with bounded potential V-1(x) + V-2(y) + epsilon W(x, y), where V-1 is a real potential, V-2 and W are compactly supported complex potentials, and epsilon is a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrodinger operator H-1 = -d(2)/ dx(2) + V-1(x) consists of a pair of isolated eigenvalues and the essential spectrum of the operator H-2 = -d(2)/ dy(2)+V-2(y) has a virtual level at its lower edge and a spectral singularity inside. Additionally, we assume that there is a certain superposition of eigenvalues of the operator H-1 with the virtual level and spectral singularity of the operator H-2; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
DIFFERENTIAL EQUATIONS
ISSN
0012-2661
e-ISSN
1608-3083
Volume of the periodical
59
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
5
Pages from-to
278-282
UT code for WoS article
000988284500011
EID of the result in the Scopus database
2-s2.0-85160648982