It is shown that the chaotic orbits in the saturated states of nonlinear three-wave coupling can be controlled by applying a new resonance, via a small sinusoidal anti-Stokes wave, to the system. For a given set of linear frequency mismatch and growth-damping parameters, any desired periodic orbit can be achieved by a proper adjustment of the amplitude of the control wave. This method is illustrated by numerical simulations. \textcopyright{} 1996 The American Physical Society.

Controlling chaos in nonlinear three-wave coupling.

The saturation of explosive instabilities by third order terms is studied analytically and by means of computer in the coherent phase description. The combined effect of nonlinear frequency shifts and effective nonlinear dissipation is considered. The stabilized explosions are found to be repetitive in general.

Repetitive Explosive Instabilities

Results from kinetic theory are reformulated in order to generalize previous equations for wave-wave interactions in magnetized plasmas.

Parametric Instabilities of Waves in Magnetized Plasmas

Integrability of double three-wave interaction

Transition to chaos in the conservative four-wave parametric interactions

The dynamics of four non-linearly interacting coherent magnetohydrodynamic (MHD) waves (plasmons) is investigated. Exact analytical solutions are obtained which describe the time behaviour of the amplitudes and phases of the waves. The analysis of the solutions shows that they vary periodically. The periods of variation are also found for various types of coherent interacting MHD waves.

Dynamics of the non-linear interaction of magnetohydrodynamic waves

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Dynamics of the non-linear interaction of magnetohydrodynamic waves