Airy-type bichromatic wave pulses on the sea surface and generation of rogue waves

Abstract

We present a theoretical study of bichromatic weakly non-collinear Airy-type waves propagating with various amplitudes in water of infinite depth. The coupled nonlinear Schrödinger equations are invoked to study the behavior of self- and cross-interacting Airy wave packets. We demonstrate that bichromatic pulses possess the main properties of single Airy wave packets—shape invariance and self-acceleration or self-deceleration—when propagating in a dispersive medium. Accounting for nonlinearity leads to a strong dependence of the structure, stability, and propagation velocity of wave pulses on their amplitude. We show that interacting pulses of Airy-type waves can form giant accelerating and decelerating waves.