Travelling waves of discrete nonlinear Schrödinger equations with nonlocal interactions

Abstract

Existence and bifurcation results are derived for quasi periodic travelling waves of discrete nonlinear Schrödinger equations with nonlocal interactions and with polynomial-type potentials. Variational tools are used. Several concrete nonlocal interactions are studied as well.

Keywords:

• nonlocal interactions
• discrete Schrödinger equation
• travelling wave
• symmetry

AMS Subject Classifications::

• 34K14
• 37K60
• 37L60

Acknowledgements

Michal Fečkan is partially supported by the Grants VEGA-MS 1/0098/08 and VEGA-SAV 2/7140/27. Vassilis Rothos is partially supported by Research Grant-International Relations of AUTH.