{"title":"Breather and rogue wave solutions for the variable coefficient nonlinear Schrödinger equation on Jacobian elliptic function periodic backgrounds","authors":"Meng-Chu Wei, Xiao-Yong Wen","doi":"10.1016/j.aml.2025.109524","DOIUrl":null,"url":null,"abstract":"<div><div>This study concentrates on exact solutions on the Jacobian elliptic function periodic background to the variable-coefficient nonlinear Schrödinger (vcNLS) equation. Through constructing the new eigenvalue solution for Lax pair and using the known Darboux transformation (DT) of vcNLS equation, the breather and rogue wave (RW) structures on Jacobian elliptic function backgrounds are revealed. By changing the variable coefficients in the equation, some novel localized wave structures are discussed graphically. The results presented in this letter will provide a valuable theoretical support for solving localized waves on the complicated seed background of variable coefficient nonlinear equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109524"},"PeriodicalIF":2.9000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000746","RegionNum":2,"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
This study concentrates on exact solutions on the Jacobian elliptic function periodic background to the variable-coefficient nonlinear Schrödinger (vcNLS) equation. Through constructing the new eigenvalue solution for Lax pair and using the known Darboux transformation (DT) of vcNLS equation, the breather and rogue wave (RW) structures on Jacobian elliptic function backgrounds are revealed. By changing the variable coefficients in the equation, some novel localized wave structures are discussed graphically. The results presented in this letter will provide a valuable theoretical support for solving localized waves on the complicated seed background of variable coefficient nonlinear equations.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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