The modulational instability (Benjamin-Feir instability) for cylindrical and spherical NLS equations (c/sNLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equation are emphasized.

Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

FEDELE, RENATO;
2010

Abstract

The modulational instability (Benjamin-Feir instability) for cylindrical and spherical NLS equations (c/sNLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equation are emphasized.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/365608
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