  In this work, the inverse scattering transform of the three-component coupled
Sasa-Satsuma equation is investigated via the Riemann-Hilbert method. Firstly
we consider a Lax pair associated with a $7\times 7$ matrix spectral problem
for the equation. Then we present the spectral analysis of the Lax pair, from
which a kind of Riemann-Hilbert problem is formulated. Moreover, $N$-soliton
solutions to the equation are constructed through a particular Riemann-Hilbert
problem with vanishing scattering coefficients. Finally, the dynamics of the
soliton solutions are discussed with some graphics.
