For the DNLS lattice with next-to-nearest-neighbour interactions, the exponentially small translational eigenvalue is derived, with on-site states stable and inter-site states unstable for µ > -1/4, and no localized states for µ < -1/4.
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Borel-Pad\'e exponential asymptotics for the discrete nonlinear Schr\"odinger model with next-to-nearest neighbour interactions
For the DNLS lattice with next-to-nearest-neighbour interactions, the exponentially small translational eigenvalue is derived, with on-site states stable and inter-site states unstable for µ > -1/4, and no localized states for µ < -1/4.