Abstract
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.
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