Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation

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.

To appear in Proceedings of the 15 Conference on Pseudo-Hermitian Hamiltonians in Quantum Physics, May 18-23 2015, Palermo, Italy (Springer Proceedings in Physics, 2016)

References in corpus (4)

• Visualization of Branch Points in PT-Symmetric Waveguides
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• An explicitly solvable model of the spontaneous PT-symmetry breaking

Cited by in corpus (3)

• Nonlinear switching and solitons in PT-symmetric photonic systems
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetric and antisymmetric nonlinear states in a split potential box