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

作　　者：Wenxiu MA 马文秀(Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;Department of Mathematics,King Abdulaziz University,Jeddah 21589,Saudi Arabia;Department of Mathematics and Statistics,University of South FloridaTampa,FL 33620-5700,USA;School of Mathematical and Statistical Sciences,North-West University,Mafikeng Campus,Private Bag X2046,Mmabatho 2735,South Africa)

机构地区：[1]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China [2]Department of Mathematics,King Abdulaziz University,Jeddah 21589,Saudi Arabia [3]Department of Mathematics and Statistics,University of South FloridaTampa,FL 33620-5700,USA [4]School of Mathematical and Statistical Sciences,North-West University,Mafikeng Campus,Private Bag X2046,Mmabatho 2735,South Africa

出　　处：《Acta Mathematica Scientia》2022年第1期127-140,共14页数学物理学报（B辑英文版）

基　　金：supported in part by NSFC(11975145 and 11972291);the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。

摘　　要：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.

关 键 词：matrix spectral problem nonlocal reverse-time integrable equation integrable hierarchy Riemann-Hilbert problem inverse scattering transform soliton solution 

分 类 号：O175.29[理学—数学]