The N-soliton solutions of the n-component generalized Sasa-Satsuma system: Riemann-Hilbert method

Using the Riemann-Hilbert method, the paper systematically investigates the n-component generalized Sasa-Satsuma system. By utilizing the Tu scheme, we systematically construct the n-component generalized Sasa-Satsuma integrable hierarchy, and obtain the Lax pair of the n-component generalized Sasa-Satsuma system. Then we give the spectral analysis of the Lax pair, from which a Riemann-Hilbert problem is formulated. Moreover, by solving the particular Riemann-Hilbert problem with vanishing scattering coefficients, N-soliton solutions are obtained for the n-component generalized Sasa-Satsuma system. Furthermore, for $n=3$, we graphically present the structures of the single-soliton and double-soliton solutions by selecting appropriate parameters.