On the Riemann-Hilbert problem for the Chen-Lee-Liu derivative nonlinear Schr\"{o}dinger equation

In this work, we investigated a combined Chen-Lee-Liu derivative nonlinear Schr"{o}dinger equation(called CLL-NLS equation by Kundu) on the half-line by unified transformation approach. We gives spectral analysis of the Lax pair for CLL-NLS equation, and establish a matrix Riemann-Hilbert problem, so as to reconstruct the solution $r(z,t)$ of the CLL-NLS equation by solving. Furthermore, the spectral functions are not independent, but enjoy by a compatibility condition, which is the so-called global relation.