Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.1, pp.34-42

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.1, pp.34-42

Modulation Instability in a Nonlinear Dispersive Medium Near Cut-Off Frequency
A.A.Balyakin, N.M.Ryskin

Modulation (Benjamin-Feir) instability of propagating quasi-harmonic wave in a nonlinear dispersive medium near cut-off frequency is analyzed. It is shown, that the increasing of wave amplitude causes the transition from convective to absolute instability. Physically this phenomena is explained by expansion of instability region to the area of backward waves, that have negative group velocity. The results of numerical simulations that verify the developed theory are presented. Application of the theory to the problem of soliton tunnelling is discussed.
Key words: modulation instability, spatio-temporal chaos, convective/absolute instability, soliton tunnelling

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