Claude, C.; Latifi, A.; Leon, J. Nonlinear resonant scattering and plasma instability: An integrable model. (English) Zbl 0744.76056 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. Cited in 18 Documents 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 PDF BibTeX XML Cite \textit{C. Claude} et al., J. Math. Phys. 32, No. 12, 3321--3330 (1991; Zbl 0744.76056) Full Text: DOI References: [1] DOI: 10.1016/0375-9601(91)91088-U · doi:10.1016/0375-9601(91)91088-U [2] DOI: 10.1103/PhysRevLett.54.2230 · doi:10.1103/PhysRevLett.54.2230 [3] DOI: 10.1103/PhysRevLett.66.2625 · 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 · doi:10.1016/0375-9601(90)90512-M [6] DOI: 10.1063/1.527859 · Zbl 0682.58041 · doi:10.1063/1.527859 [7] DOI: 10.1063/1.527859 · Zbl 0682.58041 · doi:10.1063/1.527859 [8] DOI: 10.1063/1.527859 · Zbl 0682.58041 · doi:10.1063/1.527859 [9] DOI: 10.1088/0305-4470/23/8/013 · Zbl 0713.35084 · doi:10.1088/0305-4470/23/8/013 [10] Zakharov V. E., Sov. Phys. JETP 34 pp 62– (1972) [11] DOI: 10.1143/PTP.52.886 · doi:10.1143/PTP.52.886 [12] Manakov S. V., Sov. Phys. JETP 56 pp 37– (1983) [13] DOI: 10.1103/PhysRevLett.66.1587 · doi:10.1103/PhysRevLett.66.1587 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.