Riemann-Hilbert method and N-soliton solutions for the mixed Chen-Lee-Liu derivative nonlinear Schr\"{o}dinger equation

In this paper, we aim to investigate the mixed Chen-Lee-Liu derivative nonlinear Schr"{o}dinger(CLL-NLS) equation via the Riemann-Hilbert(RH) method. we construct a RH problem base on the Jost solution of the Lax pair. By solving this RH problem corresponding to the non reflection case, the N-soliton solution of CLL-NLS equation is obtained, which expression is the ratio of $(2N+1)\times (2N+1)$ determinant and $2N\times 2N$ determinant.