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Statistical approach of the modulational instability of the discrete self-trapping equation

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Abstract.

The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view, considering the oscillator amplitude as a random variable. A kinetic equation for the two-point correlation function is written down, and its linear stability is studied. Both a Gaussian and a Lorentzian form for the initial unperturbed wave spectrum are discussed. Comparison with the continuum limit (NLS equation) is carried out.

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Authors and Affiliations

  1. Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering "Horia Hulubei", Magurele, PO Box MG-6, Bucharest, Romania

    A. Visinescu & D. Grecu

Authors
  1. A. Visinescu
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  2. D. Grecu
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Correspondence to A. Visinescu.

Additional information

Received: 29 May 2003, Published online: 4 August 2003

PACS:

63.70.+h Statistical mechanics of lattice vibrations and displacive phase transitions - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.45.Yv Solitons

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Visinescu, A., Grecu, D. Statistical approach of the modulational instability of the discrete self-trapping equation. Eur. Phys. J. B 34, 225–229 (2003). https://doi.org/10.1140/epjb/e2003-00215-3

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  • DOI: https://doi.org/10.1140/epjb/e2003-00215-3

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