Quasiperiodic localized oscillating solutions in the discrete nonlinear Schrödinger equation with alternating on-site potential

Magnus Johansson and Andrey V. Gorbach
Phys. Rev. E 70, 057604 – Published 18 November 2004

Abstract

We present an example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a nonintegrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schrödinger equation with alternating on-site energies, modeling, e.g., an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed “pulsons,” are found to exist in continuous families ranging arbitrarily close to both the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.

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  • Received 18 December 2003

DOI:https://doi.org/10.1103/PhysRevE.70.057604

©2004 American Physical Society

Authors & Affiliations

Magnus Johansson1,* and Andrey V. Gorbach2,†

  • 1Department of Physics and Measurement Technology, Linköping University, S-581 83 Linköping, Sweden
  • 2Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany

  • *Electronic address: mjn@ifm.liu.seURL: http://www.ifm.liu.se/∼majoh
  • Electronic address: gorbach@mpipks-dresden.mpg.de

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Issue

Vol. 70, Iss. 5 — November 2004

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