Riemann-Hilbert approach and N-soliton solutions for a generalized Sasa-Satsuma equation

A generalized Sasa-Satsuma equation on the line is studied via the Riemann-Hilbert approach. Firstly we derive a Lax pair associated with a 3×3 matrix spectral problem for the generalized Sasa-Satsuma equation. 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 problems with vanishing scattering coefficients, N-soliton solutions are obtained for the generalized Sasa-Satsuma equation. In addition, the N-soliton solutions of the generalized Sasa-Satsuma equation are reduced to those of the Sasa-Satsuma equation and a new complex mKdV equation, respectively.