广义Sasa-Satsuma方程在半直线上的初边值问题

董凤娇; 胡贝贝

doi:10.3969/j.issn.1000-5641.2019.04.004

广义Sasa-Satsuma方程在半直线上的初边值问题

doi: 10.3969/j.issn.1000-5641.2019.04.004

董凤娇^1,,
胡贝贝^2, ,

1.
滁州学院计算机与信息工程学院, 安徽滁州 239000
2.
滁州学院数学与金融学院, 安徽滁州 239000

基金项目:

国家自然科学基金 11601055

安徽省高校优秀青年人才基金 gxyq2019096

安徽省高校自然科学研究项目 KJ2019A0637

详细信息

作者简介:
董凤娇, 女, 硕士, 助教, 从事计算机符号计算研究.E-mail:dfjjfd@163.com

通讯作者:
胡贝贝, 男, 博士, 讲师, 从事孤立子与可积系统研究.E-mail:hu_chzu@163.com

中图分类号: O175.29
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- 文章访问数: 97
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- PDF下载量: 89
- 被引次数: 0
出版历程
- 收稿日期: 2018-08-14
- 刊出日期: 2019-07-25

An initial-boundary value problem for the generalized Sasa-Satsuma equation on the half-line

DONG Feng-jiao^1
,,
HU Bei-bei^{2
, ,}

1.
School of Computer and Information Engineering, Chuzhou University, Chuzhou Anhui 239000, China
2.
School of Mathematics and Finance, Chuzhou University, Chuzhou Anhui 239000, China

摘要

摘要: 本文基于Fokas统一变换方法分析了广义Sasa-Satsuma方程在半直线上的初边值问题.假设广义Sasa-Satsuma方程的解$ u(x, t) $存在, 证明了其初边值问题的解可用复谱参数$ \lambda $平面上的$ 3\times3 $矩阵Riemann-Hilbert问题的形式解唯一表示.
- Riemann-Hilbert问题 /
- 广义Sasa-Satsuma方程 /
- 初边值问题 /
- Fokas统一变换
Abstract: In this paper, we implement the Fokas unified transform method to study initial-boundary value problems of the generalized Sasa-Satsuma equation on the half-line. Assuming that the solution $ u(x, t) $ of the generalized Sasa-Satsuma equation exists, we will prove that it can be expressed in terms of the unique solution of a $ 3\times3 $ matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $ \lambda $.
- Riemann-Hilbert problem /
- generalized Sasa-Satsuma equation /
- initialboundary value problems /
- Fokas unified transform

HTML全文

图 1 $ (x, t) $-平面中的三条曲线$ \gamma_1, \gamma_2, \gamma_3 $

Fig. 1 The three contours $ \gamma_1, \gamma_2, \gamma_3 $ in the $ (x, t) $-domaint

下载: 全尺寸图片幻灯片

图 2 复$ \lambda $-平面中的集合$ \{D_j\}_1^4 $

Fig. 2 The sets $ \{D_n\}_1^4, $ which decompose the complex $ \lambda $-plane

下载: 全尺寸图片幻灯片

参考文献(18)

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