Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa–Satsuma case

We present the lowest order rogue wave solution of the Sasa–Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of the Peregrine solution appears when the extension parameter of the SSE is reduced to zero. -- Highlights: ► For the first time a rogue wave solution of the Sasa–Satsuma equation is presented. ► It is given by fourth order polynomials rather than second order in the NLSE limit. ► SSE rogue waves are illustrated for various parameters, as deviation from the NLSE. ► A non-singular NLSE limit of a solution of the SSE has been demonstrated.