Singular instability of exact stationary solutions of the nonlocal Gross-Pitaevskii equation

Abstract

In this paper we show numerically that for nonlinear Schrodinger type systems the presence of nonlocal perturbations can lead to a beyond-all-orders instability of stable solutions of the local equation. For the specific case of the nonlocal one-dimensional Gross-Pitaevskii equation with an external standing light wave potential, we construct exact stationary solutions for an arbitrary interaction kernel. As the nonlocal and local equations approach each other (by letting an appropriate small parameter $\epsilon \to 0$), we compare the dynamics of the respective solutions. By considering the time of onset of instability, the singular nature of the inclusion of nonlocality is demonstrated, independent of the form of the interaction kernel.

4 pages, 4 figures

References in corpus (3)

• Modulational instability in nonlocal nonlinear Kerr media
• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Loop structure of the lowest Bloch band for a Bose-Einstein condensate

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• Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
• On Nonlocal Gross-Pitaevskii Equations with Periodic Potentials
• Vortices in nonlocal Gross-Pitaevskii equation
• Symmetry breaking bifurcation in Nonlinear Schrodinger /Gross-Pitaevskii Equations