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/content/aip/journal/jmp/57/9/10.1063/1.4962417
2016-09-16
2016-09-27

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 -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.

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