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In 1925 Cherry discussed two oscillators of positive and negative energy that are nonlinearly coupled in a special way, and presented exact solutions of the nonlinear equations showing explosive instabilities independent of the strength of the nonlinearity and the initial amplitudes. In this paper Cherry's Hamiltonian is transformed into a form which allows a simple physical interpretation. The new Hamiltonian is generalised to three nonlinearly coupled oscillators; it corresponds to three-wave interaction in a continuum theory, like the Vlasov-Maxwell theory, if linear negative energy waves exist.

Additional information

Authors: PFIRSCH D, Max-Planck-Institut für Plasmaphysik, Garching bei München (DE)
Bibliographic Reference: Report: IPP 6/290 EN (1990) 4 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199011040 / Last updated on: 1994-12-01
Original language: en
Available languages: en
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