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Instabilities via negative Krein signature in a weakly non-Hamiltonian DNLS model

Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
$^\dagger$This contribution is part of the Special Issues: Hamiltonian Lattice Dynamics
  Guest Editors: Simone Paleari; Tiziano Penati
  Link: http://www.aimspress.com/newsinfo/1165.html

Special Issues: Hamiltonian Lattice Dynamics

In the present work we consider a model that has been proposed at the continuum level for self-defocusing nonlinearities in atomic Bose-Einstein condensates (BECs) in order to capture phenomenologically the loss of condensate atoms to thermal ones. We explore a model combining dispersion, nonlinearity and gain/loss at the discrete level, and illustrate the idea that modes associated with negative “energy” (mathematically: negative Krein signature) can give rise to instability of excited states when non-Hamiltonian terms are introduced in a nonlinear dynamical lattice. We showcase this idea by considering one-, two- and three-site discrete modes, exploring their stability via analytical approximations, and corroborating their continuation numerically over the relevant parameter controlling the strength of the weakly non-Hamiltonian term. We also manifest through direct numerical simulations their unstable nonlinear dynamics.
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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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