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

Propagation of a narrow-band three-frequency finite amplitude wave (wavepacket) with a symmetric frequency spectrum and arbitrary ratio of initial amplitudes and phases is studied experimentally. It is shown, that at propagation in fresh water every Fourier-component of a wavepacket gets the additional phase incursion caused by nonlinear interaction between them. Dispersive characteristics: changes of different harmonics phase speeds, group speed of a wavepacket and dispersive parameter are calculated from the obtained relationships. It is found, that occurrence of a nonlinear dispersion directly depends on amount of three-frequency wave phase invariant, which is a linear combination of initial phases of harmonic waves in a wavepacket. It is shown, that change of phase invariant may affect both on size and on sign of dispersion. Conditions when it is possible to exclude dispersion are examined. Experimental setup, method and measurement conditions for study of nonlinear phase incursions are considered. The qualitative agreement of computed and experimental results is obtained.