Eur. Phys. J. B 34, 225-229 (2003)
https://doi.org/10.1140/epjb/e2003-00215-3

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

Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering “Horia Hulubei”, PO Box MG-6, Mǎgurele, Bucharest, Romania

Corresponding author: ^a avisin@theory.nipne.ro

Received: 8 January 2003
Revised: 29 May 2003
Published online: 4 August 2003

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.