Abstract
The full description of the nonlinear interaction between positive-energy and negative-energy waves in a dispersive medium is derived with the use of the concept of quasi-particles. The generalized Manley-Rowe relations in terms of the occupation numbers (actions) of positive-energy and negative-energy quasi-particles (waves) are obtained in a dispersive medium. The extended rate-equations are also obtained, which describe the temporal and spatial variation of the numbers of quasi-particles. As an interesting case for the nonlinear negative-energy instability, the three-wave interaction is discussed, in which a signal wave excited by a pumping wave has a convective or an absolute instability with the help of a negative-energy idler wave.
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