Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry

Dohnal, Tomáš; Siegl, Petr (2016). Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry. Journal of mathematical physics, 57(9), 093502. American Institute of Physics 10.1063/1.4962417

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Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear symmetry, like e.g. the PT-symmetry, of the problem. Under this condition we show that the nonlinear eigenvalues bifurcating from real linear eigenvalues remain real and the corresponding nonlinear eigenfunctions remain symmetric. The abstract results are applied in a number of physical models of Bose-Einstein condensation, nonlinear optics and superconductivity, and further numerical analysis is performed.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Siegl, Petr

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-2488

Publisher:

American Institute of Physics

Funders:

[4] Swiss National Science Foundation

Projects:

Projects 0 not found.

Language:

English

Submitter:

Petr Siegl

Date Deposited:

11 Jul 2017 16:46

Last Modified:

11 Jul 2017 16:46

Publisher DOI:

10.1063/1.4962417

ArXiv ID:

1504.00054

BORIS DOI:

10.7892/boris.97808

URI:

https://boris.unibe.ch/id/eprint/97808

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