The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for tm waves propagating in a layer with arbitrary nonlinearity

The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue t...

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Vydané v:Computational mathematics and mathematical physics Ročník 53; číslo 1; s. 78 - 92
Hlavní autori: Valovik, D. V., Zarembo, E. V.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht SP MAIK Nauka/Interperiodica 01.01.2013
Springer Nature B.V
Predmet:
Approximation
Boundary value problems
Cauchy problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Eigenvalues
Electric fields
Electromagnetism
Geometry
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Nonlinearity
Ordinary differential equations
Physics
Propagation
Studies
Theorems
Wave propagation
approximate method for computation of eigenvalues
Maxwell equations
nonlinear eigenvalue transmission problem
Cauchy problem
ISSN:0965-5425, 1555-6662
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Shrnutí:The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue transmission problem for a system of two ordinary differential equations. A theorem on the existence and localization of at least one eigenvalue is proven. On the basis of this theorem, a method for finding approximate eigenvalues of the considered problem is proposed. Numerical results for Kerr and saturation nonlinearities are presented as examples.
Bibliografia:SourceType-Scholarly Journals-1
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513010089