Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations
arXiv:nlin/0610030 · doi:10.1007/s10773-006-9265-2
Abstract
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is found. The modulational instability is associated with a positive imaginary part of the frequency. The integral equation is solved for different types of initial distributions (delta-function, Lorentzian) and the results are compared with those obtained using a deterministic approach. The differences between modulation instability of the normal NLS equation and derivative NLS equations is emphasized.
16 pages, 4 figures, accepted for publication in Int. J. Theor. Phys