Please use this identifier to cite or link to this item:
http://dx.doi.org/10.25673/38130
Title: | Eigenvalue bifurcation in doubly nonlinear problems with an application to surface plasmon polaritons |
Author(s): | Dohnal, Tomáš![]() Romani, Giulio |
Issue Date: | 2021 |
Type: | Article |
Language: | English |
Abstract: | We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter (“doubly” nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the linear problem using a Lyapunov–Schmidt reduction and provide an expansion of both the nonlinear eigenvalue and the solution. We further prove that if the linear eigenvalue is real and the nonlinear problem PT-symmetric, then the bifurcating nonlinear eigenvalue remains real. These general results are then applied in the context of surface plasmon polaritons (SPPs), i.e. localized solutions for the nonlinear Maxwell’s equations in the presence of one or more interfaces between dielectric and metal layers. We obtain the existence of transverse electric SPPs in certain PT-symmetric configurations. |
URI: | https://opendata.uni-halle.de//handle/1981185920/38373 http://dx.doi.org/10.25673/38130 |
Open Access: | ![]() |
License: | ![]() |
Sponsor/Funder: | Publikationsfond MLU |
Journal Title: | Nonlinear differential equations and applications |
Publisher: | [Springer International Publishing AG] |
Publisher Place: | [Cham (ZG)] |
Volume: | 28 |
Original Publication: | 10.1007/s00030-020-00668-2 |
Appears in Collections: | Open Access Publikationen der MLU |
Files in This Item:
File | Description | Size | Format | |
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Dohnal-Romani2021_Article_EigenvalueBifurcationInDoublyN.pdf | 863.74 kB | Adobe PDF | ![]() View/Open |