Abstract
The modulational dynamics of a small amplitude, high frequency dispersive wavetrain, coupled to acoustic waves is addressed in the framework of the Zakharov-Rubenchik equations. The influence of the Mach number (ratio of the group velocity of the carrying waves to the sound velocity), of the strength of the acoustic wave coupling, of the Doppler shift and of the direction of the modulation (quasi-longitudinal in the example of Alfvén waves in dispersive MHD, quasi-transverse in the context of laser hot spots) is analyzed. At small Mach number, an early adiabatic regime takes place, followed, when the coupling to acoustic waves is insufficient to arrest the collapse, by another singular regime strongly sensitive to the Doppler shift, during which intense fronts for the hydrodynamic quantities develop and lead to a shift of the focus location.
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