riemann-hilbert方法deift zhou非線性速降及其應(yīng)用

報(bào)告內(nèi)初值問題求解非標(biāo)準(zhǔn)的RH方初邊值求解Fokas方長時(shí)間漸近行為RH方法/Deift-Zhou非線性速降RH方法/Deift-Zhou非線性速降四、隨機(jī)矩陣與RH方法/Deift-Zhou非線性速降五、聚焦NLS初值問題解的長時(shí)間漸近Riemann-Hilbert問題與Riemannmonodromy問題有關(guān)，1851年，首先由Riemann引入.1900年，在國際數(shù)學(xué)家大會(huì)上，Hilbert將Riemannmonodromy歸為現(xiàn)今流行的Riemann-Hilbert問題,即Hilbert所提23個(gè)問題的第21問題：具有給定奇點(diǎn)和單值群的Fuchs類線性微分方解的存在性

dy i1x1908年，Plemelj將Riemann-Hilbert問題轉(zhuǎn)化為奇異積分方程問 ，Bliru在解決Riemann-Hibe問題RHP學(xué)的強(qiáng)有力的分析工具Riem-Hileei-u非線性速降法Riemann-Hilbert方法在可積系統(tǒng)中的最大受益者：非線性程初值問題解的整體漸近分 RiemanHile粗略地講，Riemann-Hilbert問題就是在復(fù)平面上尋找一個(gè)在定曲線上具有特Beals-Cofiman理論：Riemann-HilbertProblem可解 YangJianke, 關(guān)的1+1維和2 J.Lenells,TheDegasperis-Procesiequationonthehalf-line, .(2013),122--XuJian,FanEngui,TheunifiedmethodfortheSasa-Satsumaequationonhalf-line,ProcRoyalSocA, JianXu,EnguiFan,Thethree-waveequationonthehalf-line,PhysicsLettersA378AS.UniversityofBoundaryValueProblems、InverseProblemsysis、FluidMechanics、Complex 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1981年，Its首先將stationaryphase思想用于RHP研究這種RHP的。 1993年，受經(jīng)典速降法和Its工作的啟發(fā)，Deift,Zhou直接考慮RHP，通過形變路徑,獲取可積系統(tǒng)嚴(yán)格精確解的long-time性質(zhì)。Deift;X.Zhou,AsteepestdescentmethodforoscillatoryRiemann–Hilbertproblems.AsymptoticsfortheMKdVequation,AnnalsofMath.137(1993),295-368(74pages)1992年，F(xiàn)okasIts首次建立了正交多項(xiàng)式與RHP的聯(lián)系，為RH方法研究正交 1999年，結(jié)合Fokas,Its正交多項(xiàng)式的RHP刻畫，Deift,Bleher,McLaughlin等開正交多項(xiàng)式漸近分析的全新研究方法(CPAM,1999)。2000年代BaikDeift,Johansson將Riemann-Hilbert方法應(yīng)用于組合學(xué)中隨機(jī)排，題 Universalityformathematicalandphysicalsystems,arxiv: 2someopenproblemsinrandommatrixtheoryandthetheoryofintegralesystems,arXiv:0712.0849v1PercyA.Deift,September,1945,CourantInstitute，NewYorkMemberoftheU.S.NationalAcademyof研究方向spectraltheory,integrablesystems,randommatrix1997,NSFSpecialCreativity1998,winnerofthePólya1998,aninvitedaddressattheInternationalCongressofMathematiciansinBerlin2003, 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