Riemann-Hilbert method and N-soliton solutions for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation

In this paper, we aim to investigate the mixed Chen-Lee-Liu derivative nonlinear Schrödinger(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 $2N\times2N$ determinant.

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