novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd_

novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd_

ID:14357076

大小:219.22 KB

页数:50页

时间:2018-07-28

novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd__第1页
novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd__第2页
novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd__第3页
novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd__第4页
novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd__第5页
资源描述:

《novikov s.p. solitons and geometry (lezioni fermiane, cambridge univ. press, 1994, web draft, 1993)(50s)_pd_》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库

1、Revisiondate:4/11/93SolitonsandGeometryS.P.Novikov1Lecture1Introduction.Planofthelectures.Poissonstructures.ThetheoryofSolitons(solitarywaves")dealswiththepropagationofnon-linearwavesincontinuummedia.Theirfamousdiscoveryhasbeendoneintheperiod1965-1968(

2、byM.KruscalandN.Zabuski,1965;G.Gardner,I.Green,M.KruscalandR.Miura,1967;P.Lax,1968

3、seethesurvey[8]orthebook[22]).ThefamiliarKdV(Korteweg-deVries)non-linearequationwasfoundtobeexactlysolvableinsomeprofoundnontrivialsensebytheso-calledInverseScatteringTr

4、ansform"(IST)atleastfortheclassofrapidlydecreasinginitialdata©(x):©t=6©©x¡©xxx[KdV]:Someotherfamoussystemsarealsosolvablebyanalogousprocedures.Thefollowingareexamplesof1+1-systems:©´³=sin©[SG]2i©t=¡©xx§j©j©[NS§]¢¢¢:Themostinterestingintegrable2+1-system

5、sarethefollowing:8

6、³=sin©appearedforthe¯rsttimeinaproblemof3-dimensionalgeometry:itdescribeslocallytheisometricimbed-dingsoftheLobatchevski2-planeL2(i.e.thesurfacewithconstantnegativeGaussiancurvature)intheEuclidean3-spaceR3.Here©istheanglebe-tweentwoasymptoticdirections(

7、´;³)onthesurfacealongwhichthesecond2(curvature)formiszero.IthasbeenusedbyBianchi,LieandBacklundfortheconstructionofnewimbeddings(Backlundtransformations",discoveredbyBianchi).b)Theellipticequation4©=sinh©appearedrecentlyforthedescriptionofgenus1surface

8、s(topologicaltori")inR3withconstantmeancurvature(H.Wente,1986;R.Walter,1987).Startingfrom1989F.Hitchin,U.Pinkall,N.Ercolani,H.Knorrer,E.Trubowitz,A.Bobenkousedinthis¯eldthetechniqueoftheperiodicIST"

9、see[5].Solitonsandalgebraicgeometry.a)Thereisafamous

10、connectionofSolitontheorywithalgebraicgeometry.Itappearedin1974-1975.ThesolutionoftheperiodicproblemsofSolitontheoryledtobeautifulanalyticalconstructionsinvolvingRiemannsurfacesandtheirJacobianvarieties,£-functionsandlateralsoPry

当前文档最多预览五页,下载文档查看全文

此文档下载收益归作者所有

当前文档最多预览五页,下载文档查看全文
温馨提示:
1. 部分包含数学公式或PPT动画的文件,查看预览时可能会显示错乱或异常,文件下载后无此问题,请放心下载。
2. 本文档由用户上传,版权归属用户,天天文库负责整理代发布。如果您对本文档版权有争议请及时联系客服。
3. 下载前请仔细阅读文档内容,确认文档内容符合您的需求后进行下载,若出现内容与标题不符可向本站投诉处理。
4. 下载文档时可能由于网络波动等原因无法下载或下载错误,付费完成后未能成功下载的用户请联系客服处理。