Modulational instability of some nonlinear continuum and discrete systems

Modulational instability (also known as the Benjamin‐Feir instability) of quasi‐monochromatic waves propagating in dispersive and weakly nonlinear media is a general phenomenon encountered in hydrodynamics, plasma physics, condensed matter and is responsible for the generation of robust solitary waves (sometime solitons). The statistical approach is reviewed for several nonlinear systems: the nonlinear Schrödinger equation, the discrete self‐trapping equation and Ablowitz‐Ladik equation. An integral stability equation is deduced from a linearized kinetic equation for the two‐point correlation function. This is solved for several choices of the unperturbed initial spectral function.

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