Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach
AIP conference proceedings2010pp. 1239–1244
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A. Grecu, Sergio De Nicola, R. Fedele, D. Grecu, Anca Vişinescu, Angelos Angelopoulos, Takis Fildisis
Abstract
The modulational (Benjamin‐Feir) instability for cylindrical and spherical NLS equations (c/s NLS 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 (δ‐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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