2006/10/12 by A. T. Grecu, A. Grecu, D. Grecu +2
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Meteorological Phenomena and Simulations #Nonlinear Photonic Systems #nlin.SI
paper · pdf · doi:10.1007/s10773-006-9265-2
16 pages, 4 figures, accepted for publication in Int. J. Theor. Phys
arxiv created 2006/10/12 · openalex publication_date 2007/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.