Next-nearest neighbor interaction and localized solutions of polymer chains

We study localization in polymer chains modeled by the nonlinear discrete S chrodinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction e xtending beyond the usual nearest-neighbor exchange approximation. Modulati onal instability of plane carrier waves is discussed and it is shown that l ocalization gets amplified under the influence of an enhanced interaction r adius. Furthermore, we construct exact localized solitonlike solutions of t he n-n-n interaction DNLS. To this end the stationary lattice system is cas t into a nonlinear map. The homoclinic orbits of unstable equilibria of thi s map are attributed to standing solitonlike solutions of the lattice syste m. We note that in comparison with the standard next-neighbor interaction D NLS which bears only one type of static soliton-like states (either stagger ing or unstaggering) the one with n-n-n interaction radius can support unst aggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger th e n-n-n interaction on the DNLS lattice the smaller are the maximal amplitu des of the standing solitonlike solutions and the less rapid are their expo nential decays.