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