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Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions

A. Gammal·T. Frederico·Lauro Tomio·F. Kh. Abdullaev
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Abstract

Considering the static solutions of the D-dimensional nonlinear Schroedinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D is greater or equal 2. In case D=2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse.

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A. Gammal, T. Frederico, Lauro Tomio, F. Kh. Abdullaev. 2000-02-02. Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions. https://doi.org/10.1016/s0375-9601(00)00114-6

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