NONLINEAR DYNAMICS

Zakharov equations with zeroth harmonic and a new type of modulation instability

Yu. V. Sedletskii

Institute of Physics of the National Academy of Science of Ukraine

Abstract: It has been shown that the system of Zakharov equations for the amplitudes of the first and zeroth harmonics of the waves on the surface of an ideal liquid describes not only the known type of the modulation instability of the envelope of the main harmonic with respect to harmonic perturbations with small wave vectors κ (Benjamin-Feier modulation instability), but also the modulation instability of a combination of the main and zeroth harmonics at κ values on the order of the wave vector k ₀ of the main harmonic. In contrast to the Benjamin-Feier modulation instability typical for large depths, the described modulation instability does not disappear at k ₀ h < 1.363.

PACS: 02.60.Cb, 47.15.Hg, 92.10.-c

Received: 13.08.2007
Revised: 11.09.2007

 English version: Journal of Experimental and Theoretical Physics Letters, 2007, 86:8, 502–507

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