Riemann–Hilbert approach and N-soliton solutions of the coupled generalized Sasa–Satsuma equation

We investigate the initial value problem for the coupled generalized Sasa–Satsuma equation. Firstly, based on the spectral analysis from Lax pair, we obtain desired analytic spectral functions, and a Riemann–Hilbert problem on the real line is formulated. Solving the special Riemann–Hilbert problem with reflectionless case, the N-soliton solutions of the coupled generalized Sasa–Satsuma equation are derived. In addition, by choosing suitable parameters, the structures of single-soliton solution and double-soliton solution are graphically presented.