Geodesic
The~initial-boundary value for the~combined Schr\"{o}dinger and Gerdjikov--Ivanov equation on the~half-line via the~Riemann--Hilbert approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 258-273

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The Fokas method is used to study the initial-boundary value problem for the combined Schrödinger and Gerdjikov–Ivanov equation on the half-line. Assuming that the solution $u(x,t)$ exists, it can be represented by the unique solution of a matrix Riemann–Hilbert problem formulated on the plane of the complex spectral parameter $\xi$. The jump matrices are given on the basis of the spectral functions, which are not independent, but are related by a global relation.
Keywords: Riemann–Hilbert problem; combined nonlinear Schrödinger and Gerdjikov–Ivanov equation; initial-boundary value problem; unified transform method. 
@article{TMF_2021_209_2_a3,
     author = {Yan Li and Ling Zhang and Beibei Hu and Ruiqi Wang},
     title = {The~initial-boundary value for the~combined {Schr\"{o}dinger} and {Gerdjikov--Ivanov} equation on the~half-line via {the~Riemann--Hilbert} approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a3/}
}
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Yan Li; Ling Zhang; Beibei Hu; Ruiqi Wang. The~initial-boundary value for the~combined Schr\"{o}dinger and Gerdjikov--Ivanov equation on the~half-line via the~Riemann--Hilbert approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 258-273. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a3/