Next-nearest neighbor interaction and localized solutions of polymer chains

  • D. Hennig

DOI: 10.1007/s100510170260

Cite this article as:
Hennig, D. Eur. Phys. J. B (2001) 20: 419. doi:10.1007/s100510170260


We study localization in polymer chains modeled by the nonlinear discrete Schrödinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction extending beyond the usual nearest-neighbor exchange approximation. Modulational instability of plane carrier waves is discussed and it is shown that localization gets amplified under the influence of an enhanced interaction radius. Furthermore, we construct exact localized solitonlike solutions of the n-n-n interaction DNLS. To this end the stationary lattice system is cast into a nonlinear map. The homoclinic orbits of unstable equilibria of this map are attributed to standing solitonlike solutions of the lattice system. We note that in comparison with the standard next-neighbor interaction DNLS which bears only one type of static soliton-like states (either staggering or unstaggering) the one with n-n-n interaction radius can support unstaggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger the n-n-n interaction on the DNLS lattice the smaller are the maximal amplitudes of the standing solitonlike solutions and the less rapid are their exponential decays.

PACS. 63.20.Pw Localized modes – 63.20.Ry Anharmonic lattice modes – 63.20.Kr Phonon-electron and phonon-phonon interactions 

Copyright information

© EDP Sciences, Springer-Verlag 2001

Authors and Affiliations

  • D. Hennig
    • 1
  1. 1.Freie Universität Berlin, Fachbereich Physik, Institut für Theoretische Physik, Arnimallee 14, 14195 Berlin, GermanyDE

Personalised recommendations