R2,1中线性Weingarten曲面的B(a)cklund变换

本文对三维Minkowski空间R2,1中具有性质K-2mH+m2-l2=0或H=constant的类时曲面定义了一个Darboux线汇,同时得到了相应的B(a)cklund变换.     

INTEGRABLE SYSTEM AND SPACELIKE SURFACES WITH PRESCRIBED MEAN CURVATURE IN MINKOWSKI 3-SPACE

1IntroductionItiswell-knownthattheclassicalWeierstrass-EnneperrepresentationformuladescribeschinalsurfacesinEuclidean3-spaceR3intermsoftheirGaussmapsandauxiliaryholomorphicfunctions[1].Moregenerally,aremarkablerepresentationforlllulahasbeendiscoveredbyKenmotsu[2]forarbitrarysurfaCesinR3withnonvallishingmeancurvature,whichdescribesthesesurfacesintermsoftheirGaussmapsandmeancurvaturefunctions.Recently,Konopelchenko[31rediscoveredthisrepresentationformulaindifferentbutequivalentformillconnect…     

Burgers方程族的对称、Backlund变换和Painleve性质之间的联系

在孤立子理论中,对于一个非线性演化方程来说,如果通过反散射变换可化为线性问题,则称为“S可积”的(如KdV方程等);如果能通过函数和自变量变换而化为线性方程,则称之为“C可积”的。C可积方程最典型的例子就是人们熟知的Burgers方程。至今已对它有了很多研究,如它具有无穷多个能构成一个无穷维李代数的对称,还具有Backlund变换和Painleve性质等等。     

BCKLUND TRANSFORMATION OF NONLINEAR EVOLUTION EQUATIONS

Using Lax pair and looking for the gauge transformation,we obtain the B(?)cklundtransformation in another form(sometimes it is called Darboux transformation)for some nonlinearevolution equations.We shall see that it is more convenient to use this form of B(?)cklundtransformation.     

扩展的Boussinesq系统Lax对的Backlund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统.首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Backlund变换.然后,又导出了Lax对的特征函数的生成公式.最后,利用Backlund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式.利用此递推公式,求出了一些Lax对的解.     

SOME NONLINEAR EVOLUTION EUQATIONS WITH LAX PAIR OF 3×3 MATRICES

For some NEEs with Lax pairs of 3×3 matrices, the author presents the B cklund transformations (in Darboux form) and the corresponding Modified equations. The method deriving the B cklund transformations and the Modified equations can be considered as an extension and development of the mehtod in [1].     

An Invariant Group of CDF Equation

CDF equation.甲。=甲二二二+2尹呈+6刀2甲:sin22切(1)15 related to the MkdV equationq。=q二二二+6口Zq二(2)(口==一(梦二+叮sinZ尹)or口二切二一刀sinZ甲)[”2],In this PaPer,grouP of CDF equation(1)。we Present an invariant,·t”·‘。,,。W‘·g,尹‘·(。rjf“)二···S·…”‘tr一yP·‘m“‘二‘一“。一“二‘it 15 taken definitely.Lemma If卯15 a solution of(1),then__l/「___。_J、___:_八_._,___八_.。_,___。_c-一叹tl‘U毖乙留“人刀一甲二之匕1“乙甲十甲云GU。乙甲十石,I一co吕乙钾一了I一cUS一乙…     

BCKLUND TRANSFORMATION ON SURFACESWITH CONSTANT MEAN CURVATURE IN R~(2.1)

In this paper, the authors obtain the Backlund transformation on time-likesurfaces with constant mean curvature in R~(2,1). Using this transformation, families ofsurfaces with constant mean curvature from known ones can be constructed.