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

Magnus Johansson, Andrey V. Gorbach

Research output: Contribution to journalArticle


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.

Original languageEnglish
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
Publication statusPublished - 18 Nov 2004

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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