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

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.