On the Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation with step-like initial data  

作　　者：Bei-Bei Hu Ling Zhang Zu-Yi Shen Ji Lin 

机构地区：[1]School of Mathematics and Finance,Chuzhou University,Anhui 239000,China [2]Applied Mathematics Research Center,Chuzhou University,Anhui 239000,China [3]Department of Physics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Communications in Theoretical Physics》2025年第2期30-38,共9页理论物理通讯(英文版)

基　　金：supported by the National Natural Science Foundation of China under Grant No.12147115;the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046;the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202;the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Province;the Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。

摘　　要：In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.

关 键 词：nonlocal Hirota equation Cauchy problem Riemann-Hilbert problem step-like initial data 

分 类 号：O17[理学—数学]