RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

doi:10.1007/s10473-022-0106-z

Abstract

Abstract: The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrödinger (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.

Key words: matrix spectral problem, nonlocal reverse-time integrable equation, integrable hierarchy, Riemann-Hilbert problem, inverse scattering transform, soliton solution

CLC Number:

37K15

Wenxiu MA. RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES[J].Acta mathematica scientia,Series B, 2022, 42(1): 127-140.

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