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In this paper, we consider the initial-boundary value problem of theKundu-Eckhaus equation on the half-line by using of the Fokas unified transformmethod. Assuming that the solution $u(x,t)$ exists, we show that it can beexpressed in terms of the unique solution of a matrix Riemann-Hilbert problemformulated in the plane of the complex spectral parameter $\lambda$. Moreover,we also get there exist spectral functions are not independent and they aresatisfying the so-called global relation.

A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line