Muller Boundary Integral Equations in the Microring Lasers Theory

The current paper clarifies the connection between the generalized complex-frequency eigenvalue problem and the corresponding nonlinear eigenvalue problem for the set of Muller integral equations posed on two disjoint closed curves. It is proved that the last problem has no solutions if the original...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-06, Vol.42 (6), p.1402-1412
Main Authors: Repina, A. I., Oktyabrskaya, A. O., Karchevskii, E. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Boundary integral method
Eigenvalues
Geometry
Integral equations
Lasers
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:The current paper clarifies the connection between the generalized complex-frequency eigenvalue problem and the corresponding nonlinear eigenvalue problem for the set of Muller integral equations posed on two disjoint closed curves. It is proved that the last problem has no solutions if the original problem and a specially tailored eigenvalue problem do not have solutions. This result is important for using the Muller boundary integral equations in the microring lasers theory.
ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022106024X