Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation

Abstract

We use spectral analysis to reduce Cauchy problem for the coupled Sasa-Satsuma equation to a 5 × 5 matrix Riemann-Hilbert problem. The upper and lower triangular factorisations of the jump matrix and a decomposition of the vector-valued spectral function are given. Applying various transformations related to the Riemann-Hilbert problems and suitable decompositions of the jump contours and the nonlinear steepest descent method, we establish the long-time asymptotics of the problem.