Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level

TL;DR

This paper reveals a mechanism allowing coupled nonlinear Schrödinger systems to produce rogue waves with peak amplitudes up to a thousand times the background, confirmed through exact solutions and numerical simulations.

Contribution

It provides explicit vector rational solutions demonstrating how rogue waves of unprecedented amplitude can form in coupled nonlinear systems.

Findings

Peak amplitudes up to a thousand times background achieved

Exact solutions obtained via Darboux-dressing transformation

Robustness confirmed under noisy and chaotic conditions

Abstract

We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrodinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field.