{"title":"Efficient Conformal Multi-Symplectic Structure-Preserving Method for Two-Dimensional Damped Nonlinear Schrödinger Equation","authors":"Yiyang Luo, Linghua Kong, Meng Chen, Xiuling Yin","doi":"10.1002/mma.70927","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, an efficient conformal multi-symplectic structure-preserving method is proposed for two-dimensional damped nonlinear Schrödinger equation. The method decomposes the original equation into several tractable one-dimensional subproblems by the splitting method, and then solves them separately and alternatively, and combines the resulting schemes by an appropriate method lastly. Moreover, the spatial derivatives are discretized with a high-order compact scheme which uses fewer grid nodes to achieve higher accuracy and improve the computational efficiency. Based on this framework, an efficient conformal multi-symplectic algorithm is developed for the equation. Some numerical experiments are reported to verify the effectiveness of the new scheme.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 16","pages":"17304-17318"},"PeriodicalIF":2.0000,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.70927","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2026/8/4 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, an efficient conformal multi-symplectic structure-preserving method is proposed for two-dimensional damped nonlinear Schrödinger equation. The method decomposes the original equation into several tractable one-dimensional subproblems by the splitting method, and then solves them separately and alternatively, and combines the resulting schemes by an appropriate method lastly. Moreover, the spatial derivatives are discretized with a high-order compact scheme which uses fewer grid nodes to achieve higher accuracy and improve the computational efficiency. Based on this framework, an efficient conformal multi-symplectic algorithm is developed for the equation. Some numerical experiments are reported to verify the effectiveness of the new scheme.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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