Nonlinear resonant scattering and plasma instability: An integrable model. (English) Zbl 0744.76056

Claude, C.; Latifi, A.; Leon, J.

J. Math. Phys. 32, No. 12, 3321-3330 (1991).

Summary: A detailed study of a system of coupled waves is given for which an initial-boundary value problem is solved by means of the spectral transform theory. This system represents the nonlinear interaction of an electrostatic high-frequency wave with the ion acoustic wave in a two component homogeneous plasma. As a result the plasma instability is understood as (i) a continuous secular transfer of energy from the laser beam to the acoustic wave, (ii) the evolution toward the formation of local singularities of the electrostatic wave (collapsing), (iii) a mutual trapping of the acoustic wave and the scattered Langmuir wave.

MSC:

76E25	Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30	Nonlinear effects in hydrodynamic stability
76X05	Ionized gas flow in electromagnetic fields; plasmic flow

Keywords:

coupled waves; spectral transform theory; nonlinear interaction; electrostatic high-frequency wave; ion acoustic wave; local singularities; scattered Langmuir wave

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