Long-time asymptotics of a three-component coupled nonlinear Schrodinger system

Starting from a specific example of 4 x 4 matrix spectral problems, an integrable coupled hierarchy, which includes a three-component coupled nonlinear Schrodinger system as the first nonlinear one, is generated, and an associated oscillatory Riemann-Hilbert problem is formulated. With the nonlinear steepest descent method, the leading long-time asymptotics for the Cauchy problem of the three-component coupled nonlinear Schrodinger system is computed, through deforming the oscillatory Riemann-Hilbert problem into a model one which is solvable. (C) 2020 Elsevier B.V. All rights reserved.