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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.

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30 Nonlinear effects in hydrodynamic stability
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
Full Text: DOI
[1] DOI: 10.1016/0375-9601(91)91088-U
[2] DOI: 10.1103/PhysRevLett.54.2230
[3] DOI: 10.1103/PhysRevLett.66.2625
[4] Zakharov V. E., Sov. Phys. JETP 35 pp 908– (1972)
[5] DOI: 10.1016/0375-9601(90)90512-M
[6] DOI: 10.1063/1.527859 · Zbl 0682.58041
[7] DOI: 10.1063/1.527859 · Zbl 0682.58041
[8] DOI: 10.1063/1.527859 · Zbl 0682.58041
[9] DOI: 10.1088/0305-4470/23/8/013 · Zbl 0713.35084
[10] Zakharov V. E., Sov. Phys. JETP 34 pp 62– (1972)
[11] DOI: 10.1143/PTP.52.886
[12] Manakov S. V., Sov. Phys. JETP 56 pp 37– (1983)
[13] DOI: 10.1103/PhysRevLett.66.1587
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