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1.
一类偏微分方程的Hamilton正则表示   总被引:13,自引:0,他引:13  
主要给出一系列关于力学中的偏微分方程的无穷维Hamilton正则表示.其中包括变系数线性偏微分方程,KdV方程,MKdV方程,KP方程,Bousinesq方程等的无穷维Hamilton正则表示.  相似文献   

2.
广义Hamilton系统的研究概况   总被引:1,自引:1,他引:0  
赵晓华  程耀 《力学进展》1994,24(3):289-300
用广义Poisson括号直接定义的广义Hamilton系统是经典Hamilton系统的一种推广。由于它的维数没有限制,同时它又保持了经典Hamilton系统的主要性质,因此具有更大的普遍性和广泛的应用前景。本文简要介绍了广义Hamilton系统理论的发展历史、基本概念和研究现状。  相似文献   

3.
朱位秋  黄志龙 《力学进展》2000,30(4):481-494
近几年中,利用Hamilton系统的可积性与共振性概念及Poisson括号性质等,提出了高斯白噪声激励下多自由度非线性随机系统的精确平稳解的泛函构造与求解方法,并在此基础上提出了等效非线性系统法,提出了拟Hamilton系统的随机平均法,并在该法基础上研究了拟Hamilton系统随机稳定性、随机分岔、可靠性及最优非线性随机控制,从而基本上形成了一个非线性随机动力学与控制的Hamilton理论框架.本文简要介绍了这方面的进展.  相似文献   

4.
高阶紧致格式求解二维粘性不可压缩复杂流场   总被引:3,自引:0,他引:3  
修东滨  任安禄 《力学学报》1996,28(3):264-269
提出了一种求解二维不可压缩复杂流场的高精度算法.控制方程为原始变量、压力Poisson方程提法.在任意曲线坐标下,采用四阶紧致格式求解Navier-Stokes方程组,时间推进采用交替方向隐式(ADI)格式,在非交错网格上用松弛法求解压力Poisson方程.对于复杂的流场,采用了区域分解方法,并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场.利用该算法计算了二维受驱空腔流动,弯管流动和垂直平板的突然起动问题.计算结果与实验结果和其他研究者的计算结果相比较吻合良好.对于平板起动流动,成功地模拟了流场中旋涡的生成以及Karman涡街的形成  相似文献   

5.
REDUCTIVE PERTURBATION METHOD OF SUPER KdV EQUATIONS   总被引:1,自引:1,他引:0  
IntroductionSuperKdVequationsareut-buux 3hhx uxxx =0 ,ht-buhx-ahux chxx =0 ,( 1 )wherea ,b,c(c≠ 0 )areconstants.Thesimilarsolutionsof ( 1 )weregivenin [1 ]bydirectmethodpresentedbyClarksonandKruskal.Inthispaper,( 1 )arechangedintoordinaryKdVequationsbyreductiveperturbationm…  相似文献   

6.
IntroductionTheexistenceofpeakonTWSofanonlinearwaveequationρt =bux 12 [(u2 ±u2 x) ρ] x, ρ =u±uxx ( 1 )wasconsideredbreiflybyP .Rosenau (see [1 ] ) .Eq.( 1 )isfoundby“reshuffling”Hamiltonianoperatorofbi_HamiltionianstructureinKdVandmKdVequation (see [2 ] ) .BecauseEq.( 1 )hasstron…  相似文献   

7.
IntroductionDuringthecourseofstudyingthewaterwave,manycompletelyintegrablemodelswereobtained ,suchasKdVequation ,mKdVequation ,(2 1 )_dimensionalKPequation ,coupledKdVequations,variantBoussinesqequations ,WKBequationsetc .[1- 13 ].Inordertofindexpliticexactsolutio…  相似文献   

8.
本文利用平均方程研究受扰MKdV-Burges方程的静态和全局动态分岔,得到了出现各种分岔的条件,揭示了该系统周期解的变化过程及其非线性动力学性质。  相似文献   

9.
IntroductionDuringthestudyofshallowwaterwaves,peopleobtainedmanywell_knowncompletelyintegrablemodels,suchasKdVequation,mKdVequation,Boussinesqequation,Whitham_Broer_KaupequationandKhokhlov_Zabolotskayaequationetc.[1~8].For2 1_dimensionalvariablecoefficientg…  相似文献   

10.
张瑞萍  孙家驹 《力学季刊》1996,17(3):233-238
本文用摄动法导出了弦的非线性振动的K-dV方程,讨论了只有耗散和色散的特殊情况,然后详细讨论了K-dV方程的孤波解的性态,并给出了弦的非线性振动孤波的主要特征。  相似文献   

11.
一类新型正则方程对广义经典力学的推广   总被引:9,自引:0,他引:9  
乔永芬 《力学学报》1990,22(1):99-105
本文首先将一类新型正则方程推广到广义经典力学,得到广义正则方程,确定泊松括号和拉格朗日括号及它们的性质,用泊松括号表示广义正则方程,建立新型Hamilton广义变分原理、Hamilton-jacobi方程。  相似文献   

12.
Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.  相似文献   

13.
The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of singularities of the Poisson operator defining the Poisson bracket. The kernel of the Poisson operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the Poisson operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the Poisson operator (the “dimension” of the center) changes. The problem is an infinite-dimension generalization of the theory of singular differential equations. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.  相似文献   

14.
In this paper, the direct method is used to find the first integrals and two new solvable cases of the Euler–Poisson equations are given.  相似文献   

15.
ANEWMETHODFORTHECONSTRUCTIONOFINTEGRABLEHAMILTONIANSYSTEMSGaoPuyun(高普云)(DepartmentofMathematics,NanjingUniversity,Nanijing210?..  相似文献   

16.
In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painlevé equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.  相似文献   

17.
A new method for the construction of integrable Hamiltonian system is proposed. For a given Poisson manifold, the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1], and obtains further new integrable Hamiltonian systems. The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones[2–4]. Two examples are given.  相似文献   

18.
The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper on simple gases (I), we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error. In two subsequent papers (II–III), we extended our original simple gas work to encompass binary gas mixture computations of the viscosity, thermal conductivity, diffusion, and thermal diffusion coefficients to high-order. In a fourth paper (IV) we derived general summational representations for the diffusion- and thermal conductivity-related bracket integrals and provided compact, explicit expressions for all of these bracket integrals needed to compute the diffusion- and thermal conductivity-related transport coefficients up to order 5 in the Sonine polynomial expansions used. In all of this previous work we retained the full dependence of our solutions on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals up to the final point of solution via matrix inversion. The elements of the matrices to be inverted are, in each case, determined by appropriate combinations of bracket integrals which contain, in general form, all of the various dependencies. Since accurate expressions for the needed bracket integrals have not previously been available in the literature beyond orders 2 or 3, and since such expressions are necessary for any extensive program of computations of the transport coefficients involving Sonine polynomial expansions to higher orders, we have investigated alternative methods of constructing appropriately general bracket integral expressions that do not rely on the term-by-term, expansion and pattern matching techniques that we developed for our previous work. It is our purpose in this paper to report the results of our efforts to obtain useful, alternative, general expressions for the bracket integrals associated with the viscosity-related Chapman–Enskog solutions for gas mixtures. Specifically, we have obtained such expressions in summational form that are conducive to use in high-order viscosity coefficient computations for arbitrary gas mixtures and have computed and reported explicit expressions for all of the orders up to 5.  相似文献   

19.
The gist of extended irreversible thermodynamics and generalized hydrodynamics is presented within the context of rheology of complex molecules (e.g., polymers) in this paper. Then, the constitutive equation for stress developed for polyatomic fluids in a previous paper is applied to rheology of polymeric fluids. This constitutive equation is fully consistent with the thermodynamic laws. It is shown that the collision bracket integrals appearing in the constitutive equation can be recast in terms of friction tensors of beads and equilibrium force-force correlation functions if the momentum relaxation is much faster than the configuration relaxation and there exist such relaxation times. The force-force correlation functions reduce to those related to the mean square radius of gyration of the polymer if the Hookean model is taken for forces. By treating the recast collision bracket integrals in the constitutive equation as empirical parameters, we analyze some experimental data on shear rate and elongation rate dependence of polymeric melts and obtain excellent agreement with experiment. We show that the empirical parameters can be related to the zero shear rate viscosity and the ratio of the secondary to the primary normal stress coefficient. Therefore, for the plane Couette flow geometry considered in the paper, the constitutive equation is completely specified by the limiting material functions at zero shear rate and relaxation times.Work supported in part by the Natural Sciences and Engineering Research Council of Canada and Fonds FCAR, Quebec. This paper was presented at the Symposium on Recent Developments in Structured Continua II held at Magog, Quebec, Canada, May 23–25, 1990.  相似文献   

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