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

A. T. Grecu·D. Grecu·Anca Visinescu
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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.

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A. T. Grecu, D. Grecu, Anca Visinescu. 2006-10-12. Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schroedinger Equations. https://doi.org/10.1007/s10773-006-9265-2

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