Long-time asymptotics for the Sasa-Satsuma equation via nonlinear steepest descent method

We formulate a $3\times 3$ Riemann-Hilbert problem to solve the Cauchy problem for the Sasa-Satsuma equation on the line, which allows us to give a representation for the solution of Sasa-Satsuma equation. We then apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Sasa-Satsuma equation.