The Unified Transform Method to Initial-Boundary Value Problem for a Coupled Cubic–Quintic Nonlinear Schrödinger System
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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 \(3\times 3\) matrix Riemann–Hilbert problem formulated in the complex \(\lambda \)-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).
KeywordsRiemann–Hilbert problem Initial-boundary value problem Coupled cubic–quintic nonlinear Schrödinger system Unified transform method
Mathematics Subject Classification37K10 35Q51 35Q15
This work was supported by the NSF of China under the Grant Nos. 11601055 and 11805114, NSF of Anhui Province of China under the Grant No. 1408085QA06, Education Department scientific research project of Anhui Province under the Grant No. KJ2017B10.
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