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We present a Riemann-Hilbert problem formalism for the initial-boundary valueproblem for the Sasa-Satsuma(SS) equation on the finite interval. Assume thatthe solution existes, we show that this solution can be expressed in terms ofthe solution of a $3\times 3$ Riemann-Hilbert problem. The relevant jumpmatrices are explicitly given in terms of the three matrix-value spectralfunctions $s(k)$, $S(k)$ and $S_L(k)$, which in turn are defined in terms ofthe initial values, boundary values at $x=0$ and boundary values at $x=L$,respectively. However, for a well-posed problem, only part of the boundaryvalues can be prescribed, the remaining boundary data cannot be independentlyspecified, but are determined by the so-called global relation. Here, weanalyze the global relation to characterize the unknown boundary values interms of the given initial and boundary data.

The unified transform method for the Sasa-Satsuma equation on the interval