Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations

Details Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations

2006-10-12

arxiv.org/abs/nlin/0610030v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 4 figures, accepted for publication in Int. J. Theor. Phys

Scientific paper

10.1007/s10773-006-9265-2

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.

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