Abstract
We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii equation with an attractive cubic nonlinearity. The trapping potential has the form of two \(\delta \)-function wells, where one well loses particles while the other one is fed with atoms at an equal rate. The parameters of the constructed solutions are expressible in terms of the roots of a system of two transcendental algebraic equations. We also furnish a simple analytical treatment of the linear Schrödinger equation with the PT -symmetric double-\(\delta \) potential.
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Acknowledgments
This contribution is a spin-off from the project on the jamming anomaly in \({ PT}\) -symmetric systems [4]; we thank Vladimir Konotop for his collaboration on the main part of the project. Nora Alexeeva’s numerical assistance and Holger Cartarius’ useful remarks are gratefully acknowledged. This work was supported by the NRF of South Africa (grants UID 85751, 86991, and 87814) and the FCT (Portugal) through the grants UID/FIS/00618/2013 and PTDC/FIS-OPT/1918/2012.
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Barashenkov, I.V., Zezyulin, D.A. (2016). Localised Nonlinear Modes in the PT-Symmetric Double-Delta Well Gross-Pitaevskii Equation. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_8
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DOI: https://doi.org/10.1007/978-3-319-31356-6_8
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