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

The Cauchy problem of the three-component derivative nonlinear Schrodinger equation is turned into a 4 x 4 matrix Riemann-I filbert 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 Schrodinger equation is obtained with the aid of the Deift-Zhou nonlinear steepest descent method.