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 firstname.lastname@example.org
Revised: 29 May 2003
Published online: 4 August 2003
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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003