The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation

The initial value problem for the Sasa-Satsuma equation is transformed to a 3×3 matrix Riemann-Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function ρ(k) are given, from which the long-time asymptotics for the Sasa-Satsuma equation with decaying initial data is obtained by using the nonlinear steepest descent method.