简介:WeconstructaclassofintegrablegeneralizationofTodamechanicswithlong-rangeinteractions.ThesesystemsareassociatedwiththeloopalgebrasL(Cr)andL(Dr)inthesensethattheirLaxmatricescanberealizedintermsofthec=0representationsoftheaffineLiealgebrasCr(1)andDr(1)andtheinteractionspatterninvolvedbearsthetypicalcharactersofthecorrespondingrootsystems.WepresenttheequationsofmotionandtheHamiltonianstructure.Thesegeneralizedsystemscanbeidentifiedunambiguouslybyspecifyingtheunderlyingloopalgebratogetherwithanorderedpairofintegers(n,m).Itturnsoutthatdifferentsystemsassociatedwiththesameunderlyingloopalgebrabutwithdifferentpairsofintegers(n1,m1)and(n2,m2)withn2<n1andm2<m1canberelatedbyanestedHamiltonianreductionprocedure.Forallnontrivialgeneralizations,theextracoordinatesbesidesthestandardTodavariablesarePoissonnon-commute,andwheneithernorm≥3,thePoissonstructurefortheextracoordinatevariablesbecomessomeLiealgebra(i.e.theextravariablesappearlinearlyontheright-handsideofthePoissonbrackets).Inthequantumcase,suchgeneralizationswillbecomesystemswithnoncommutativevariableswithoutspoilingtheintegrability.
简介:P427.12002032384信标光波长对全场补偿的影响=Effectofbeaconwavelengthonfullfieldcompensation[刊,中]/李有宽,杜祥琬,陈栋泉(北京应用物理与计算数学研究所.北京(100088))//强激光与粒子束.-2001,13(5).-541-544激光在近水平长距离传输时,闪烁效应会影响自适应光学的校正效果。在Rytov近似下,导出了纯相位补偿方差和全场补偿方差与信标光波长的关系,研究了信标光波长对补偿效果的影响。结果表明,当信标光的波长与主激光波长之比小于1.89时,全场补偿的方差小