LAUSR

In this study, we consider a coupled cubic–quintic nonlinear Schrödinger (CCQNLS) system, which is an important model in fiber-optic communication since this system can be used to describe the effect of quintic nonlinearities on the propagation of ultrashort optical soliton pulses in non-Kerr media. We solved the initial-boundary value problem of the CCQNLS system on the half-line by virtue of the unified transform method. And we manifest that the solution of the CCQNLS system can be represented by the unique solution of a $$3\times 3$$3×3 matrix Riemann–Hilbert problem formulated in the complex $$\lambda $$λ-plane. Furthermore, we demonstrate that a slice of spectral functions are not independent of each other, but rather to satisfy a paramount relations (so-called global relationship).