Abstract
The three-component Sasa–Satsuma equation associated with the 7 × 7 matrix spectral problem is studied by using the Riemann–Hilbert method. The spectral analysis of the Lax pair is performed for the three-component Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. As applications, N-soliton solutions for the three-component Sasa–Satsuma equation are obtained by solving the Riemann–Hilbert problems corresponding the reflectionless case. Furthermore, a compact form of N-soliton solutions formula is given explicitly, which is the ratio of (2N + 1) × (2N + 1)-determinant and (2N × 2N)-determinant.
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