{"title":"Algebro-geometric integration to the discrete Chen–Lee–Liu system","authors":"Xiaoxue Xu , Decong Yi , Xing Li , 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.
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.