文献类型：期刊文献

英文题名：The revised Riemann-Hilbert approach to the Kaup-Newell equation with a non-vanishing boundary condition: Simple poles and higher-order poles

作者：Zhang, Yongshuai[1];Qiu, Deqin[2];Shen, Shoufeng[3];He, Jingsong[4]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China;[2]Huizhou Univ, Sch Math & Stat, Huizhou 516007, Guangdong, Peoples R China;[3]Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China;[4]Shenzhen Univ, Inst Adv Study, Shenzhen 518060, Guangdong, Peoples R China

年份：2024

卷号：65

期号：8

外文期刊名：JOURNAL OF MATHEMATICAL PHYSICS

收录：SCI-EXPANDED(收录号：WOS:001299159900003)、、Scopus(收录号：2-s2.0-85201874118)、WOS

基金：This work is supported by the National Natural Science Foundation of China (Grant Nos. 12171433 and 12071304) and Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515013106).

语种：英文

外文摘要：With a non-vanishing boundary condition, we study the Kaup-Newell (KN) equation (or the derivative nonlinear Schr & ouml;dinger equation) using the Riemann-Hilbert approach. Our study yields four types of Nth order solutions of the KN equation that corresponding to simple poles on or not on the rho circle (rho related to the non-vanishing boundary condition), and higher-order poles on or not on the rho circle of the Riemann-Hilbert problem (RHP). We make revisions to the usual RHP by introducing an integral factor that ensures the RHP satisfies the normalization condition. This is important because the Jost solutions go to an integral factor rather than the unit matrix when the spectral parameter goes to infinity. To consider the cases of higher-order poles, we study the parallelization conditions between the Jost solutions without assuming that the potential has compact support, and present the generalizations of residue conditions of the RHP, which play crucial roles in solving the RHP with higher-order poles. We provide explicit closed-form formulae for four types of Nth order solutions, display the explicit first-order and double-pole solitons as examples and study their properties in more detail, including amplitude, width, and exciting collisions.