Abstract
The instabilities of nonlinear waves with a square-root dispersion ω ∼ | k | are studied. We present a new type of instability that affects wavelengths of the order of the carrier wave. This instability can initiate the formation of collapses and of narrow pulses. • A new type of wave instability is presented. • This instability can affect nonlinear waves with concave dispersion. • The instability leads to modulations that have shorter wavelengths than the carrier wave. • This instability can initiate strongly nonlinear events.
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