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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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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description 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.
doi_str_mv 10.1134/S199508022106024X
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source Springer Nature
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
title Muller Boundary Integral Equations in the Microring Lasers Theory
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