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

The modulational instability (MI) in the class of NLS equations is discussed using a statistical approach (SAMI). 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 wi...

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Bibliographic Details
Main Authors: A. T. Grecu, D. Grecu, Anca Visinescu
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Published: 2006
Subjects:
sami
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.6566
http://arxiv.org/pdf/nlin/0610030v1.pdf
Description
Summary:The modulational instability (MI) in the class of NLS equations is discussed using a statistical approach (SAMI). 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 (δ- function, Lorentzian) and the results are compared with those obtained using a deterministic approach (DAMI). The differences between MI of the normal NLS equation and derivative NLS equations is emphasized. Keywords:NLS equations, modulational instability PACS: 05.45 1.

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