关于一类相对论准线性薛定谔方程的数值解法

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-06-05 DOI:10.1007/s41980-024-00895-8

Canwei Huang, Youjun Wang

{"title":"关于一类相对论准线性薛定谔方程的数值解法","authors":"Canwei Huang, Youjun Wang","doi":"10.1007/s41980-024-00895-8","DOIUrl":null,"url":null,"abstract":"<p>We study the numerical solutions for a class of quasilinear Schrödinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schrödinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations\",\"authors\":\"Canwei Huang, Youjun Wang\",\"doi\":\"10.1007/s41980-024-00895-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the numerical solutions for a class of quasilinear Schrödinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schrödinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.</p>\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-024-00895-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00895-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了一类准线性薛定谔方程的数值解法，该方程产生于大功率超短激光在物质中的自通道，与具有非线性原理部分的能量函数相关，因此不能直接使用经典算法。通过变量置换法将准线性薛定谔方程转换为半线性椭圆方程，然后应用数值山越算法。还进行了一些数值实验，包括零势、非零恒势和奇异问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

查看原文本刊更多论文

On Numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

We study the numerical solutions for a class of quasilinear Schrödinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schrödinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.