Abstract
In the nonlinear interaction between three waves described by coupled-mode equations, the waves interact by continuously transferring energy between themselves, resulting in bounded periodic solutions for the individual wave envelopes. However, when three waves interact with pulse widths sufficiently narrow so that their pulse durations are commensurate with the characteristic time for the interaction, steady state pulse profiles result and the three wave envelopes propagate as solitons. This latter aspect of nonlinear wave propagation is studied. Starting with the couple-mode equations, these soliton solutions are derived and the theory is applied to the nonlinear interactions between upper- and lower-hybrid waves and electron and ion Bernstein modes propagating in a warm magnetized plasma. Half widths for the solitons are calculated together with estimates of their speed of propagation which are computed for some typical laboratory plasmas.
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