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

We formulate a 3 × 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 the Sasa–Satsuma equation. We then apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Sasa–Satsuma equation.