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Dispersive Oscillations in a System of Three Interacting Waves

Three-wave interaction among positive and negative energy modes as well as among three modes with the same energy sign has been studied in the presence of second order dispersive effects. In the case of positive and negative energy modes a nonlinear frequency shift from third order nonlinear terms has been taken into account in order to obtain limited solutions. The second order dispersive effects have been found to have a strong tendency to introduce oscillations in the wave amplitudes and phases. These oscillations have been described analytically and are found primarily to concern only the mode on which they are excited. To second order they may couple to the oscillations of the other modes and may then grow resonantly. To first order the wave energy is not influenced by the oscillations.