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In this letter we examine the two-component Hirota (TH) equations whichdescribes the pulse propagation in a coupled fiber with higher-order dispersionand self-steepening. As the TH equations is a complete integrable system, whichadmits a $3\times 3$ Ablowitz-Kaup-Newell-Segu(AKNS)-type Lax pair, we obtainthe general N-soliton solutions of the TH equations via the Riemann-Hilbert(RH)method when the jump matrix of a specific RH problem is a $3\times3$ unitmatrix. As an example, the expression of one- and two-soliton are displayedexplicitly.

Riemann-Hilbert method and soliton solutions in the system of two-component Hirota equations