Self-accelerating rogue waves

Abstract

We present a theoretical study of bichromatic weakly non-collinear Airy-type waves propagating with various amplitudes in water of infinitedepth. The coupled nonlinear Schrödinger equations are invoked to study the behavior of self- and cross-interacting Airy wave packets. Wedemonstrate that bichromatic pulses possess the main properties of single Airy wave packets—shape invariance and self-acceleration or selfdeceleration—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 acceleratingand decelerating waves. The study of accelerating and decelerating bichromatic wave pulses of the Airy type significantly expands theset of scenarios for the occurrence of rogue waves in various physical media.