Riemann–Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equation

The Cauchy problem of the three-component derivative nonlinear Schrödinger equation is turned into a 4× 4 matrix Riemann–Hilbert problem by utilizing the spectral analysis. Through a transformation of the spectral parameters, a reduced Riemann–Hilbert problem is derived. Two distinct factorizations of the jump matrix for the reduced Riemann–Hilbert problem and a decomposition of the vector spectral function are deduced. The leading-order asymptotics of the solution for the Cauchy problem of the three-component derivative nonlinear Schrödinger equation is obtained with the aid of the Deift–Zhou nonlinear steepest descent method.