CONCENTRATION OF COUPLED CUBIC NONLINEAR SCHRDINGER EQUATIONS

IntroductionThe following coupled cubic nonlinear Schr dinger equations inR2are considered:it-Δ=(||2-|ψ|2),t>0,x∈R2,iψt-Δψ=(-||2 |ψ|2)ψ,t>0,x∈R2,(1)where=(t,x):[0,T)×R2→C,ψ=ψ(t,x):[0,T)×R2→C,Δis the Laplaceoperator onR2.The e     

ATTRACTORS OF NONAUTONOMOUS SCHR?DINGER EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｔｒａｃｔｏｒｓｏｆａｕｔｏｎｏｍｏｕｓｅｖｏｌｕｔｉｏｎｅｑｕａｔｉｏｎｓｈａｖｅｂｅｅｎｉｎｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｔｈｅｍａｔｉｃａｌｌｉｔｅｒａｔｕｒｅ (ｓｅｅ,ｆｏｒｅｘａｍｐｌｅ ,ｂｏｏｋｓ [1 ] ,[2 ] ,[3 ] ,[4 ]ａｎｄｔｈｅｌｉｔｅｒａｔｕｒｅｃｉｔｅｄｔｈｅｒｅ) .Ｔｈｅｎｏｎａｕｔｏｎｏｍｏｕｓｉｎｆｉｎｉｔｅ＿ｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓｗｅｒｅｌｅｓｓｗｅｌｌｕｎｄｅｒｓｔｏｏｄ .Ｉｎ 1 994 ,Ｃｈｅｐｙｚｈ…     

DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRDINGER SYSTEM

Introduction WeconsidertheperturbedcouplednonlinearSchr dingerequations(CNLS)iq1t=q1xx 2[|q1|2 |q2|2-ω2]q1 iε(^D1q1-r1),iq2t=q2xx 2[|q1|2 |q2|2-ω2]q2 iε(^D2q2-r2),(1)whereqjis2πperiodicandeveninx.rjisconstant,^Djisboundeddissipativeoperatorand assumedtotaketheform^Djqj=-αjqj βj^Bqj,(2)αjandβjarepositiveconstants,j=1,2.^BisaFouriertruncationofLaplaceoperator xx,i.e.,^Bcos(kx)=-k2cos(kx),k0isasmallperturbation parameter.Th…     

THE EXACT SOLITARY WAVE SOLUTIONS FOR THE KLEIN-GORDON-SCHRDINGER EQUATIONS

The solitary wave solutions for the Klein-Gordon-Schrdinger Equations were obtained by using the homogeneous balance principle. The form of the solutions is more generalized than the result that has been proved by pure theoretical and qualitative method in literature; namely, the form of solutions in literature is a particular case of result of the present paper.     

THE EXACT SOLITARY WAVE SOLUTIONS FOR THE KLEIN- GORDON-SCHRDINGER EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐｒｅｓｅｎｔｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｃｏｕｐｌｅｄＫｌｅｉｎ＿Ｇｏｒｄｏｎ＿Ｓｃｈｒ ｄｉｎｇｅｒ (ＫＧＳ)ｅｑｕａｔｉｏｎｓａｓｆｏｌｌｏｗｓ:ｉψｔ+ 12 Δψ=-φψ ,φｔｔ-Δφ+ｍ2 φ=｜ψ｜2 .( 1 )( 2 )( 1 )ａｎｄ ( 2 )ｄｅｓｃｒｉｂｅａｃｌａｓｓｉｃａｌｍｏｄｅｌｏｆｉｎｔｅｒａｃｔｉｏｎｏｆｎｕｃｌｅｏｎｆｉｅｌｄｗｉｔｈｍｅｓｏｎｆｉｅｌｄ[1],ｗｈｅｒｅψｉｓａｃｏｍｐｌｅｘｓｃａｌａｒｎｕｃｌｅｏｎｆｉｅｌｄ ,φ＿ａｒｅａｌｍｅｓｏｎｆｉ…     

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＯｗｉｎｇｔｏｔｈｅｆａｃｔｔｈａｔｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅＤｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｓｆｏｒａｃｌａｓｓｏｆｓｙｓｔｅｍｓｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｔｈｅｆｏｒｍｕ″=ｖ ,εｖ″ ｆ(ｘ ,ｕ ,ｕ′)ｖ′ -ｇ(ｘ ,ｕ ,ｕ′)ｖ=0　　 ( 0 <ｘ <1,0 <ε 1) ,ｕ( 0 ;ε) =0 ,ｕ( 1;ε) =0 ,ｖ( 0 ;ε) =α ,ｖ( 1;ε) =β,( 1)ｈａｖｅｔｈｅｑｕａｌｉｔａｔｉｖｅｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｏｆａｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｓｙｓｔｅ…     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hölder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hǒlder continuity is proved for the gradient of the solution to the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LINARD SYSTEM

IntroductionInthispaper,weconsidertheexistenceofsolutionsoffollowingboundaryvalueproblemonreallineforLi啨ｎａｒｄｓｙｓｔｅｍ :u″-f(u)u′ g(u) =0 ,u(-∞ ) =0 ,　u( ∞ ) =1 ,(1 )wheref:R →Randg :R →RarefunctionsofclassC1.Amotivationforourresearchisconne