Riemann–Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation  

作　　者：Guofei Zhang Jingsong He Yi Cheng 张国飞;贺劲松;程艺(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;Institute for Advanced Study,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China [2]Institute for Advanced Study,Shenzhen University,Shenzhen 518060,China

出　　处：《Chinese Physics B》2022年第11期164-171,共8页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.12071304 and 11871446);the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012554)。

摘　　要：We investigate the inverse scattering transform for the Schrödinger-type equation under zero boundary conditions with the Riemann–Hilbert(RH)approach.In the direct scattering process,the properties are given,such as Jost solutions,asymptotic behaviors,analyticity,the symmetries of the Jost solutions and the corresponding spectral matrix.In the inverse scattering process,the matrix RH problem is constructed for this integrable equation base on analyzing the spectral problem.Then,the reconstruction formula of potential and trace formula are also derived correspondingly.Thus,N double-pole solutions of the nonlinear Schrödinger-type equation are obtained by solving the RH problems corresponding to the reflectionless cases.Furthermore,we present a single double-pole solution by taking some parameters,and it is analyzed in detail.

关 键 词：Schrödinger-type equation Riemann-Hilbert problem zero boundary conditions N double-pole solitons 

分 类 号：O175[理学—数学]