Nonlinear dispersion of a three-frequency wave packet in nondispersive quadratically-nonlinear medium. Theory

Influence of amplitude-phase ratio in an initial spectrum on propagation of a narrow-band three-frequency wave with finite amplitude in quadratically-nonlinear medium without dispersion is considered within a framework of perturbation method. It is shown, that phase-dependent nonlinear additives to the initial waves appear in the third order. This result to phase speed changes of the separate waves in a wavepacket and to disruption of phase synchronism between them. The interaction of nonlinear processes of absorption and dispersion is found. The expression describing local behaviour of the dispersion law in a second approximation is obtained.