Phase-invariant solutions of nonlinear wave-wave interacting systems

The existence of phase-invariant solutions for a class of nonlinear wave-wave interacting systems is studied. These solutions have the property that the phase of each wave is invariant with time or unaffected by the nonlinear interactions. Explicit results are obtained for certain two-wave and three-wave systems. It is shown that for these systems, the wave-energy transfer along the phase-invariant solutions is always unidirectional. The application of these results to the non-inear interaction between two transverse waves and a longitudinal wave in a magnetized collisionless plasma is discussed.