{"title":"Discrete nonlinear Schrödinger type equations: Solutions and continuum limits","authors":"Song-lin Zhao, Xiao-hui Feng, Wei Feng","doi":"arxiv-2404.14060","DOIUrl":null,"url":null,"abstract":"As local and nonlocal reductions of a discrete second-order\nAblowitz-Kaup-Newell-Segur equation, two discrete nonlinear Schr\\\"odinger type\nequations are considered. Through the bilinearization reduction method, we\nconstruct double Casoratian solutions of the reduced discrete nonlinear\nSchr\\\"odinger type equations, including soliton solutions and Jordan-block\nsolutions.Dynamics of the obtained one-soliton and two-soliton solutions are\nanalyzed and illustrated. Moreover,both semi-continuous limit and full\ncontinuous limit, are applied to obtain solutions of the local and nonlocal\nsemi-discrete nonlinear Schr\\\"odinger type equations, as well as the local and\nnonlocal continuous nonlinear Schr\\\"odinger type equations.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Exactly Solvable and Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.14060","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
As local and nonlocal reductions of a discrete second-order
Ablowitz-Kaup-Newell-Segur equation, two discrete nonlinear Schr\"odinger type
equations are considered. Through the bilinearization reduction method, we
construct double Casoratian solutions of the reduced discrete nonlinear
Schr\"odinger type equations, including soliton solutions and Jordan-block
solutions.Dynamics of the obtained one-soliton and two-soliton solutions are
analyzed and illustrated. Moreover,both semi-continuous limit and full
continuous limit, are applied to obtain solutions of the local and nonlocal
semi-discrete nonlinear Schr\"odinger type equations, as well as the local and
nonlocal continuous nonlinear Schr\"odinger type equations.