高阶Chen-Lee-Liu方程在半直线上的初边值问题

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 422-431.

高阶Chen-Lee-Liu方程在半直线上的初边值问题

胡贝贝¹(),张玲¹(),张宁²

¹ 滁州学院数学与金融学院安徽滁州 239000
² 山东科技大学公共基础课教学部山东泰安 271019

收稿日期:2018-12-24 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:胡贝贝, E-mail:hubsquare@chzu.edu.cn|张玲, E-mail:originzhang@126.com
基金资助:
国家自然科学基金(11601055);国家自然科学基金(11805114);安徽省自然科学基金(1408085QA06);安徽省高校优秀人才基金(gxyq2019096);安徽省高校自然科学研究项目(KJ2019A0637)

An Initial-Boundary Value Problem for the Higher-Order Chen-Lee-Liu Equation on the Half-Line

Beibei Hu¹(),Ling Zhang¹(),Ning Zhang²

¹ School of Mathematics and Finance, Chuzhou University, Anhui Chuzhou 239000
² Department of Basical Courses, Shandong University of Science and Technology, Shandong Taian 271019

Received:2018-12-24 Online:2020-04-26 Published:2020-05-21
Supported by:
the NSFC(11601055);the NSFC(11805114);the NSF of Anhui Province(1408085QA06);the University Excellent Talent Fund of Anhui Province(gxyq2019096);the Natural Science Research Projects in Colleges and Universities of Anhui Province(KJ2019A0637)

摘要/Abstract

摘要：

该文运用Fokas方法分析了高阶Chen-Lee-Liu方程在半直线上的初边值问题，证明了高阶Chen-Lee-Liu方程初边值问题的解可以用复λ平面上的矩阵Riemann-Hilbert问题的形式解唯一表示.

关键词: Riemann-Hilbert问题, 高阶Chen-Lee-Liu方程, 跳跃矩阵, Fokas方法

Abstract:

In this paper, the initial-boundary value problems of the higher-order Chen-Lee-Liu (HOCLL) equation on the half-line has been analysed via the Fokas method. We show that the solution q(x, t) of HOCLL equation can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ.

Key words: Riemann-Hilbert problem, Higher-order Chen-Lee-Liu equation, Jump matrix, Fokas method

中图分类号:

O175

胡贝贝,张玲,张宁. 高阶Chen-Lee-Liu方程在半直线上的初边值问题[J]. 数学物理学报, 2020, 40(2): 422-431.

Beibei Hu,Ling Zhang,Ning Zhang. An Initial-Boundary Value Problem for the Higher-Order Chen-Lee-Liu Equation on the Half-Line[J]. Acta mathematica scientia,Series A, 2020, 40(2): 422-431.

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