Trajectory Characters of Rogue Waves

TL;DR

This paper introduces a simple method to represent rogue wave solutions and analyzes their trajectories, revealing an 'X' shape pattern and proposing a short-term prediction approach based on initial perturbations.

Contribution

It provides a new simple representation for arbitrary-order rogue waves and explicitly studies their trajectories, including a novel prediction method based on initial data.

Findings

Rogue wave trajectories form 'X' shapes.

Short-time prediction is possible through initial perturbation measurements.

Global distribution of rogue waves exhibits characteristic 'X' patterns.

Abstract

We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves. Short-time prediction on rogue wave can be done through measuring the information contained in the initial perturbation twice.