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

@inproceedings{DeconinckSingularIO,
  title={Singular instability of exact stationary solutions of the nonlocal Gross-Pitaevskii equation},
  author={Bernard Deconinck and J. Nathan Kutz}
}
In this paper we show numerically that for nonlinear Schrödinger 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… CONTINUE READING