Mathematical theory of normal waves in an open metal-dielectric regular waveguide of arbitrary cross section
The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulat...
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| Published in | Mathematical modelling and analysis Vol. 25; no. 3; pp. 391 - 408 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Vilnius
Vilnius Gediminas Technical University
13.05.2020
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| Online Access | Get full text |
| ISSN | 1392-6292 1648-3510 |
| DOI | 10.3846/mma.2020.10682 |
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| Abstract | The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found. |
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| AbstractList | The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found. Keywords: non-linear eigenvalue problem, Maxwell's equations, operator-function, Sobolev spaces, discrete spectrum. AMS Subject Classification: 34B07; 47A10; 78A50. The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found. The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found. |
| Audience | Academic |
| Author | Smirnov, Yury Smolkin, Eugene |
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| References | L.L. Helms (key-10.3846/mma.2020.10682-6) 1975 Yu.G. Smirnov (key-10.3846/mma.2020.10682-19) 2009 A.S. Zilbergleit (key-10.3846/mma.2020.10682-30) 1966 A.N Kolmogorov (key-10.3846/mma.2020.10682-10) 1999 key-10.3846/mma.2020.10682-24 key-10.3846/mma.2020.10682-25 Yu.G. Smirnov (key-10.3846/mma.2020.10682-17) 1990; 312 key-10.3846/mma.2020.10682-27 key-10.3846/mma.2020.10682-20 key-10.3846/mma.2020.10682-21 key-10.3846/mma.2020.10682-22 key-10.3846/mma.2020.10682-23 R.A. Adams (key-10.3846/mma.2020.10682-2) 1975 V.V. Lozhechko (key-10.3846/mma.2020.10682-13) 1995; 35 I.C. Gohberg (key-10.3846/mma.2020.10682-5) 1965 A.W. Snyder (key-10.3846/mma.2020.10682-26) 1983 T. Kato (key-10.3846/mma.2020.10682-8) 1980 V.S. Vladimirov (key-10.3846/mma.2020.10682-28) 1985 L. Levin (key-10.3846/mma.2020.10682-12) 1975 key-10.3846/mma.2020.10682-14 key-10.3846/mma.2020.10682-15 G.N. Watson (key-10.3846/mma.2020.10682-29) 1995 key-10.3846/mma.2020.10682-16 key-10.3846/mma.2020.10682-1 key-10.3846/mma.2020.10682-11 key-10.3846/mma.2020.10682-3 key-10.3846/mma.2020.10682-4 key-10.3846/mma.2020.10682-7 Yu.G. Smirnov (key-10.3846/mma.2020.10682-18) 1991; 27 key-10.3846/mma.2020.10682-9 |
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| Snippet | The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary... The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary... |
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| SubjectTerms | Analysis Boundary conditions Cross-sections discrete spectrum Eigenvalues Electromagnetic fields Electromagnetism Mathematical analysis Maxwell's equations non-linear eigenvalue problem operator-function Permeability Propagation Sobolev space Sobolev spaces Wave propagation Waveguides |
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| Title | Mathematical theory of normal waves in an open metal-dielectric regular waveguide of arbitrary cross section |
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