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Symmetry 2016, 8(8), 72; https://doi.org/10.3390/sym8080072

Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry

Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa P-1749-016, Portugal
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Academic Editor: Blas Manuel Rodríguez-Lara
Received: 1 July 2016 / Revised: 19 July 2016 / Accepted: 21 July 2016 / Published: 28 July 2016
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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Abstract

We consider nonlinear modes of the nonlinear Schrödinger equation with nonlocal nonlinearities and and PT -symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their linear stability in the limit of small nonlinearity. It is demonstrated that either PT symmetry or the nonlocality can be used to manage the stability of the small-amplitude nonlinear modes. The stability properties are also found to depend on the particular shape of the nonlocal kernel. Numerical simulations show that the stability results remain valid not only for the infinitesimally small nonlinear modes, but also for the modes of finite amplitude. View Full-Text
Keywords: nonlinear Schrödinger equation; nonlinear Schrödinger equation;
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zezyulin, D.A.; Konotop, V.V. Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry. Symmetry 2016, 8, 72.

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