Penrose instabilities and the emergence of rogue waves in Sasa–Satsuma equation
Department of Nonlinear Dynamics, Bharathidasan University, 620024, Tiruchirappalli, Tamil Nadu, India
2 Department of Mathematics, Indian Institute of Science, 560012, Bangalore, Karnataka, India
Accepted: 17 May 2021
Published online: 28 May 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021