Journal
THEORETICAL AND MATHEMATICAL PHYSICS
Volume 210, Issue 3, Pages 337-352Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0040577922030047
Keywords
Volterra integral equations; Riemann-Hilbert problem; matrix Lakshmanan-Porsezian-Daniel system; initial-boundary value problem; Fokas unified transform approach
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Funding
- National Natural Science Foundation of China [12147115, 11975145]
- Natural Science Foundation of Anhui Province [2108085QA09]
- Natural Science Research Project of Colleges and Universities in Anhui Province [KJ2021A1094, KJ2021B03]
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The initial-boundary value problems for the matrix Lakshmanan-Porsezian-Daniel system are studied using the Fokas unified transform approach. Spectral analysis is performed on the 4 x 4 Ablowitz-Kaup-Newell-Segur-type matrix Lax pair, and solutions of the matrix Lakshmanan-Porsezian-Daniel system are reconstructed from a 4 x 4 matrix Riemann-Hilbert problem. It is also proven that the spectral functions are related by the global relation.
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 x 4 Ablowitz-Kaup-Newell-Segur-type matrix Lax pair is performed. Second, solutions of the matrix Lakshmanan-Porsezian-Daniel system are reconstructed from a 4 x 4 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.
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