https://doi.org/10.1140/epjst/e2016-02664-1
Regular Article
Stability of gap solitons in the presence of a weak nonlocality in periodic potentials
1 Department of Mechanical Engineering, Laboratory of Nonlinear Dynamics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
2 Oceanography Center, University of Cyprus, Nicosia, Cyprus
a e-mail: rothos@auth.gr
Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016
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.
© EDP Sciences, Springer-Verlag, 2016
