159 research outputs found
Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation
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 -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 Schr\"odinger equation with the PT-symmetric
double- potential.Comment: 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
Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and symmetry
We consider nonlinear modes of the nonlinear Schr\"odinger equation with a
nonlocal nonlinearity and an additional 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.
Additional numerical simulations show that the stability results remain valid
not only for the infinitesimally small nonlinear modes, but also for the modes
of finite amplitudeComment: 11 pages, 2 figures; submitte
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