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 / A. T., Grecu; S., De Nicola; Fedele, Renato; D., Grecu; A., Visinescu. - STAMPA. - AIP Conf. Proc. vol. 1203:(2010), pp. 1239-1244. (Intervento presentato al convegno 7th International Conference of the Balkan Physical Union tenutosi a Alexandroupolis, Greece nel 09–13 September 2009) [10.1063/1.3322347].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
