Riemann–Hilbert approach and $N$-soliton solutions of the two-component Kundu–Eckhaus equation

We study the two-component Kundu–Eckhaus equation with a zero boundary condition at infinity. Based on the spectral analysis of the Lax pair, a Riemann–Hilbert problem is established. An $N$-soliton solution is then obtained by solving the regular and nonregular Riemann–Hilbert problems.