Algebro-geometric integration to the discrete Chen–Lee–Liu system

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED
Xiaoxue Xu , Decong Yi , Xing Li , Da-jun Zhang
{"title":"Algebro-geometric integration to the discrete Chen–Lee–Liu system","authors":"Xiaoxue Xu ,&nbsp;Decong Yi ,&nbsp;Xing Li ,&nbsp;Da-jun Zhang","doi":"10.1016/j.physd.2025.134778","DOIUrl":null,"url":null,"abstract":"<div><div>Algebro-geometric solutions for the discrete Chen–Lee–Liu (CLL) system are derived in this paper. We construct a nonlinear integrable symplectic map which is used to define discrete phase flows. Compatibility of the maps with different parameters gives rise to the discrete CLL system whose solutions (discrete potentials) can be formulated through the discrete phase flows. Baker-Akhiezer functions are introduced and their asymptotic behaviors are analyzed. Consequently, we are able to reconstruct the discrete potentials in terms of the Riemann theta functions. These results can be extended to 3-dimensional case and algebro-geometric solutions of the discrete modified Kadomtsev–Petviashvili equation are obtained. Some solutions of genus one case are illustrated.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134778"},"PeriodicalIF":2.7000,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278925002556","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Algebro-geometric solutions for the discrete Chen–Lee–Liu (CLL) system are derived in this paper. We construct a nonlinear integrable symplectic map which is used to define discrete phase flows. Compatibility of the maps with different parameters gives rise to the discrete CLL system whose solutions (discrete potentials) can be formulated through the discrete phase flows. Baker-Akhiezer functions are introduced and their asymptotic behaviors are analyzed. Consequently, we are able to reconstruct the discrete potentials in terms of the Riemann theta functions. These results can be extended to 3-dimensional case and algebro-geometric solutions of the discrete modified Kadomtsev–Petviashvili equation are obtained. Some solutions of genus one case are illustrated.
离散陈-李-刘系统的代数-几何积分
本文导出了离散陈-李-刘(CLL)系统的代数-几何解。构造了一个用于定义离散相流的非线性可积辛映射。不同参数映射的兼容性产生了离散的CLL系统,其解(离散势)可以通过离散相流来表示。引入了Baker-Akhiezer函数,并分析了其渐近行为。因此,我们可以用黎曼函数来重建离散势。这些结果可以推广到三维情况,得到了离散修正Kadomtsev-Petviashvili方程的代数-几何解。给出了属1情况的若干解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
期刊介绍: Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信