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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On {the~Riemann{\textendash}Hilbert} problem of the~matrix {Lakshmanan{\textendash}Porsezian{\textendash}Daniel} system with a~$4\times4$ {AKNS-type} matrix {Lax} pair},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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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/

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