Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry

Tomáš Dohnal, Petr Siegl

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
34 Downloads (Pure)

Abstract

Many physical systems can be described by eigenvalues of nonlinear equations 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, e.g., the PT-symmetry. Under the symmetry we show that the nonlinear eigenvalues bifurcating from real linear eigenvalues remain real and the corresponding nonlinear eigenfunctions remain symmetric. The abstract result is applied in a number of physical models of Bose-Einstein condensation, nonlinear optics, and superconductivity, and numerical examples are presented.

Original languageEnglish
Article number093502
JournalJournal of Mathematical Physics
Volume57
Issue number9
DOIs
Publication statusPublished - 01 Sep 2016
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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