Asymptotics for the Sasa-Satsuma equation in terms of a modified Painleve II transcendent

We consider the initial-value problem for the Sasa-Satsuma equation on the line with decaying initial data. Using a Riemann-Hilbert formulation and steepest descent arguments, we compute the long-time asymptotics of the solution in the sector vertical bar x vertical bar <= Mt(1/3) constant. It turns out that the asymptotics can be expressed in terms of the solution of a modified Painleve II equation. Whereas the standard Painleve II equation is related to a 2 x 2 matrix Riemann-Hilbert problem, this modified Painleve II equation is related to a 3 x 3 matrix Riemann-Hilbert problem. (C) 2019 The Authors. Published by Elsevier Inc.