Geodesic
On the~Riemann--Hilbert problem of the~matrix Lakshmanan--Porsezian--Daniel system with a~$4\times4$ AKNS-type matrix Lax pair
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 387-404

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The initial-boundary value problems for the matrix Lakshmanan–Porsezian–Daniel system are studied by utilizing the Fokas unified transform approach. First, the spectral analysis of the $4\times4$ Ablowitz–Kaup–Newell–Segur-type matrix Lax pair is performed. Second, solutions of the matrix Lakshmanan–Porsezian–Daniel system are reconstructed from a $4\times4$ matrix Riemann–Hilbert problem. It is proved in addition that the spectral functions are not independent but are related by the so-called global relation.
Keywords: Volterra integral equations, Riemann–Hilbert problem, matrix Lakshmanan–Porsezian–Daniel system, initial-boundary value problem, Fokas unified transform approach. 
@article{TMF_2022_210_3_a3,
     author = {Beibei Hu and Xiaomei Yu and Ling Zhang},
     title = {On {the~Riemann--Hilbert} problem of the~matrix {Lakshmanan--Porsezian--Daniel} system with a~$4\times4$ {AKNS-type} matrix {Lax} pair},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--404},
     publisher = {mathdoc},
     volume = {210},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a3/}
}
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Beibei Hu; Xiaomei Yu; Ling Zhang. On the~Riemann--Hilbert problem of the~matrix Lakshmanan--Porsezian--Daniel system with a~$4\times4$ AKNS-type matrix Lax pair. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 387-404. http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a3/