明亮非线性Schrödinger孤子对长波横向不稳定性的敏感性

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI:10.1098/rspa.2004.1330

T. Bridges

{"title":"明亮非线性Schrödinger孤子对长波横向不稳定性的敏感性","authors":"T. Bridges","doi":"10.1098/rspa.2004.1330","DOIUrl":null,"url":null,"abstract":"A new theory for transverse instability of bright solitons of equations of nonlinear Schrödinger (NLS) type is presented, based on a natural deformation of the solitons into a four–parameter family. This deformation induces a set of four diagnostic functionals which encode information about transverse instability. These functionals include the deformed power, the deformed momentum and two new functionals. The main result is that a sufficient condition for long–wave transverse instability is completely determined by these functionals. Whereas longitudinal instability is determined by a single partial derivative (the Vakhitov–Kolokolov criterion), the condition for transverse instability requires 10 partial derivatives. The theory is illustrated by application to scalar NLS equations with general potential, and vector NLS equations for optical media with ξ(2) nonlinearity.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the susceptibility of bright nonlinear Schrödinger solitons to long–wave transverse instability\",\"authors\":\"T. Bridges\",\"doi\":\"10.1098/rspa.2004.1330\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new theory for transverse instability of bright solitons of equations of nonlinear Schrödinger (NLS) type is presented, based on a natural deformation of the solitons into a four–parameter family. This deformation induces a set of four diagnostic functionals which encode information about transverse instability. These functionals include the deformed power, the deformed momentum and two new functionals. The main result is that a sufficient condition for long–wave transverse instability is completely determined by these functionals. Whereas longitudinal instability is determined by a single partial derivative (the Vakhitov–Kolokolov criterion), the condition for transverse instability requires 10 partial derivatives. The theory is illustrated by application to scalar NLS equations with general potential, and vector NLS equations for optical media with ξ(2) nonlinearity.\",\"PeriodicalId\":20722,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.2004.1330\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.2004.1330","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

摘要

提出了非线性Schrödinger型方程(NLS)亮孤子横向不稳定性的一种新理论，该理论基于孤子自然变形为四参数族。这种变形引起了一组四个诊断功能，这些功能编码了有关横向不稳定的信息。这些泛函包括变形功率、变形动量和两个新的泛函。主要结果是，这些泛函完全确定了长波横向不稳定性的充分条件。纵向不稳定性由单个偏导数(Vakhitov-Kolokolov准则)决定，而横向不稳定性的条件需要10个偏导数。通过应用于具有一般势的标量NLS方程和具有ξ(2)非线性的光介质的矢量NLS方程来说明该理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the susceptibility of bright nonlinear Schrödinger solitons to long–wave transverse instability

A new theory for transverse instability of bright solitons of equations of nonlinear Schrödinger (NLS) type is presented, based on a natural deformation of the solitons into a four–parameter family. This deformation induces a set of four diagnostic functionals which encode information about transverse instability. These functionals include the deformed power, the deformed momentum and two new functionals. The main result is that a sufficient condition for long–wave transverse instability is completely determined by these functionals. Whereas longitudinal instability is determined by a single partial derivative (the Vakhitov–Kolokolov criterion), the condition for transverse instability requires 10 partial derivatives. The theory is illustrated by application to scalar NLS equations with general potential, and vector NLS equations for optical media with ξ(2) nonlinearity.

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

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

自引率

0.00%

发文量

期刊介绍： Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.