ABSTRACT
The generalized mixed nonlinear Schrödinger (GMNLS) equation is a completely integrable model under certain parameter conditions, which has important applications in nonlinear optics, weak nonlinear dispersive water wave and quantum field theory. In this work, we use the unified transformation method to construct a Riemann-Hilbert problem and discuss the initial-boundary value problems of the GMNLS equation on the half-line. Furthermore, we also obtain that some spectral functions are not independent of each other, but meet a paramount global relation.
Acknowledgments
The authors are grateful to thank Professor Ling Zhang and Doctor Pingping Fang for helpful discussions and thanks the referees for helpful suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).