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

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

2002-12-19

arxiv.org/abs/nlin/0212043v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

10.1140/epjb/e2003-00215-3

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 done.

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