Penrose Instabilities and the Emergence of Rogue waves in Sasa-Satsuma equation

TL;DR

This paper uses Penrose stability analysis on the Wigner-transformed Sasa-Satsuma equation to identify conditions and regions where rogue waves can emerge, providing a new analytical approach to understanding their formation.

Contribution

It introduces a novel stability analysis method for the Sasa-Satsuma equation to predict rogue wave emergence and spatial localization.

Findings

Identified the region where rogue waves can emerge.

Formulated a condition for rogue wave formation.

Calculated spatial localization of rogue waves.

Abstract

In this paper, we calculate the region of emergence of rogue waves in the Sasa-Satsuma equation by performing Penrose stability analysis. We consider Wigner-transformed Sasa-Satsuma equation and separate out unstable solutions, namely Penrose instability modes. We superpose these modes in a small region. With the help of marginal property of the Wigner transform we identify the region in which rogue wave solution can emerge in the Sasa-Satsuma equation and calculate the amount of spatial localization. We also formulate a condition for the emergence of rogue wave solution in the Sasa-Satsuma equation.