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Stability of gap solitons in the presence of a weak nonlocality in periodic potentials

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Abstract

In this work, we study the stability and internal modes of one-dimensional gap solitons employing the modified nonlinear Schrödinger equation with a sinusoidal potential together with the presence of a weak nonlocality. Using an analytical theory, it is proved that two soliton families bifurcate out from every Bloch-band edge under self-focusing or self-defocusing nonlinearity, and one of these is always unstable. Also we study the oscillatory instabilities and internal modes of the modified nonlinear Schrödinger equation.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Laboratory of Nonlinear Dynamics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    I.K. Mylonas & V.M. Rothos

  2. Oceanography Center, University of Cyprus, Nicosia, Cyprus

    A.K. Rossides

Authors
  1. I.K. Mylonas
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  2. A.K. Rossides
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  3. V.M. Rothos
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Correspondence to V.M. Rothos.

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Mylonas, I., Rossides, A. & Rothos, V. Stability of gap solitons in the presence of a weak nonlocality in periodic potentials. Eur. Phys. J. Spec. Top. 225, 1187–1197 (2016). https://doi.org/10.1140/epjst/e2016-02664-1

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  • DOI: https://doi.org/10.1140/epjst/e2016-02664-1

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