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

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

2002-08-22

arxiv.org/abs/cond-mat/0208441v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 4 figures

Scientific paper

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.

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