Self-accelerating rogue waves

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 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 accelerating
and decelerating waves. The study of accelerating and decelerating bichromatic wave pulses of the Airy type significantly expands the
set of scenarios for the occurrence of rogue waves in various physical media.