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

Autor:	E. V. Zarembo, Dmitry V. Valovik
Rok vydání:	2013
Předmět:	Cauchy problem Computational Mathematics symbols.namesake Nonlinear system Maxwell's equations Plane (geometry) Surface wave Ordinary differential equation Mathematical analysis symbols Divide-and-conquer eigenvalue algorithm Eigenvalues and eigenvectors Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 53:78-92
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542513010089
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7396a7a2384b6150e944a57103496d6e https://doi.org/10.1134/s0965542513010089 Zobrazit plný text záznamu Full text from SpringerLink