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Next-nearest neighbor interaction and localized solutions of polymer chains

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  • D. Hennig

    (Freie Universität Berlin, Fachbereich Physik, Institut für Theoretische Physik, Arnimallee 14, 14195 Berlin, Germany)

Abstract

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.

Suggested Citation

  • D. Hennig, 2001. "Next-nearest neighbor interaction and localized solutions of polymer chains," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(3), pages 419-425, April.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:3:d:10.1007_s100510170260
    DOI: 10.1007/s100510170260
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    Cited by:

    1. Villegas-Martínez, B.M. & Moya-Cessa, H.M. & Soto-Eguibar, F., 2022. "Modeling displaced squeezed number states in waveguide arrays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

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