Journal
ACTA MATHEMATICA SCIENTIA
Volume 42, Issue 1, Pages 127-140Publisher
SPRINGER
DOI: 10.1007/s10473-022-0106-z
Keywords
matrix spectral problem; nonlocal reverse-time integrable equation; integrable hierarchy; Riemann-Hilbert problem; inverse scattering transform; soliton solution
Categories
Funding
- NSFC [11975145, 11972291]
- Natural Science Foundation for Colleges and Universities in Jiangsu Province [17 KJB 110020]
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This paper focuses on establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reverse-time NLS hierarchies.
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
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