{"title":"The equivalent form and the evolution of generalized Schrodinger map heat flow","authors":"Penghong, Zhong","doi":"10.12988/nade.2015.536","DOIUrl":null,"url":null,"abstract":"We present a study of the singular and smooth solutions of the generalized Schrödinger map heat flow equation (GSMF) on hyperbolic space. Considering the associated hyperbolic Landau-Lifshitz spin evolution equation with uniaxial anisotropy together with applied field, we study the dynamics in terms of the stereographic variable. Firstly, a equivalent equation of this system is obtained. Based on this equivalent equation, we construct some singular and smooth solution of GSMF in 2-dimensional H2 space. We study these norm −1 solutions that allow us depict the mechanism of the evolution. Mathematics Subject Classification: 35K10, 35K65, 35Q40, 35Q55","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis and Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/nade.2015.536","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
We present a study of the singular and smooth solutions of the generalized Schrödinger map heat flow equation (GSMF) on hyperbolic space. Considering the associated hyperbolic Landau-Lifshitz spin evolution equation with uniaxial anisotropy together with applied field, we study the dynamics in terms of the stereographic variable. Firstly, a equivalent equation of this system is obtained. Based on this equivalent equation, we construct some singular and smooth solution of GSMF in 2-dimensional H2 space. We study these norm −1 solutions that allow us depict the mechanism of the evolution. Mathematics Subject Classification: 35K10, 35K65, 35Q40, 35Q55
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
