The Riemann-Hilbert problem and long-time asymptotics for the Kundu-Eckhaus equation with decaying initial value

We present a Riemann-Hilbert problem formalism for the initial value problem of the Kundu-Eckhaus equation on the line. The long-time asymptotic for the solutions of the Kundu-Eckhaus equation is further analyzed via the Deift-Zhou nonlinear steepest descent method.