On characterizations of structural stability

This note takes a sketch of a proof of a characterization theorem for diffeomorphism on a compact 3-dimensional smooth manifold to be structurally stable.     

Monodromy and nonintegrability in complex Hamiltonian systems

This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented.     

Hamilton体系下环扇形域的Stokes流动问题

基于极坐标下Stokes流的基本方程,将径向坐标模拟为时间坐标,推导了Hamilton体系下Stokes流动问题的对偶方程,采用本征向量展开法对环扇形域Stokes流动问题进行了分析,并给出了相应的实际算例,其结果说明了本文方法的有效性。     

Projected Runge-Kutta methods for constrained Hamiltonian systems

Projected Runge-Kutta (R-K) methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations (DAEs) in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.     

THE HAMILTONIAN SYSTEM AND COMPLETENESS OF SYMPLECTIC ORTHOGONAL SYSTEM

I.IntroductionThemethodofseparationofvariablesisimportanttosolvethesoluti0n0fprobIem0fmathematicalphysics,butmanyproblen1sofmathematicalphysicscannotseparatet'ariab1es,thereforeitrestrictstheranget0appIicatemethodofseparationofvariable.Inthepaperlll,Zhong…     

Hamiltonian formulation of nonlinear water waves in a two-fluid system

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｇｅｏｍｅｔｒｉｚａｔｉｏｎｏｆｍｅｃｈａｎｉｃｓｉｓａｔｅｎｄｅｎｃｙｏｆｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｃｏｎｔｉｎｕｕｍｍｅｃｈａｎｉｃｓａｎｄｄｒａｗｓｅｘｔｅｎｓｉｖｅａｔｅｎｔｉｏｎｏｆｒｅｓｅａｒｃｈｅｒｓ...     

Plane elasticity in sectorial domain and the Hamiltonian system

ＰＬＡＮＥＥＬＡＳＴＩＣＩＴＹＩＮＳＥＣＴＯＲＩＡＬＤＯＭＡＩＮＡＮＤＴＨＥＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＺｈｏｎｇＷａｎ－ｘｉｅｔａｐ（钟万勰）（ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ．Ｄａｌｉａｎ）（ＲｅｃｅｉｖｅｄＤｅｃ．...     

Homoclinic orbits for some (2+1)-dimensional nonlinear Schr(o)dinger-like equations

Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some (2 1)dimensional nonlinear Schr6dinger-like equations are constructed based on Hirota's bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel'nikov equation, and g-Schr(o)dinger equation are constructed based on Hirota's bilinear method.     

The discussion about horseshoes and finite subharmonic bifurcations

In this paper, finite subharmonic bifurcations have been discussed by means of some examples. It is found that for centrally symmetric system, under small disturbance, if it has two independant sequences of subharmonic bifurcations, the system passes to chaos (horeseshoe) through finite subharmonic bifurcations, and that for noncentrally symmetric system, the relation between subharmonic bifurcations and horseshoe is complicated.     

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS(Ⅰ)——FUNDAMENTAL THEORY

For the first time, Hamiltonian system used in dynamics is introduced to formulate statics and Hamiltonian equation is derived corresponding to the original governing equation, which enables separation of variables to work and eigen function to be obtained for the boundary problem. Consequently, analytical and semi-analytical solutions can be got. The method is especially suitable to solve rectangular plane problem and spatial prism in elastic mechanics. The paper presents a new idea to solve partially differential equation in solid mechanics. The flexural problem and plane stress problem of laminated plate are studied in detail. This project is supported by National Natural Science Foundation of China for Post-Doctorate Research.     

Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation

The paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions.     

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF MATERIALS(Ⅲ)—FLEXURE AND FREE VIBRATION OF PLATES

The methodology presented in PartⅠis employed to deal with flexure and freevibration of anisotropic plates.     

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS'''' EQUATION

ＩｎｔｒｏｄｕｃｔｉｏｎＢｕｒｇｅｒｓ’ｅｑｕａｔｉｏｎｉｓｏｎｅｏｆｖｅｒｙｉｍｐｏｒｔａｎｔｆｌｕｉｄｅｑｕａｔｉｏｎｓ.Ｉｔｓｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｉｓｒａｔｈｅｒｔｈａｎｃｏｍｐｌｅｘｉｔｙｏｗｉｎｇｔｏｔｈｅｎｏｎｌｉｎｅａｒｔｅｒｍ .Ｔｅｍａｎｅｔａｌ.[1] ｓｔｕｄｉｅｄｔｈｅｅｘｉｓｔｅｎｃｅｏｆａｇｌｏｂａｌａｔｔｒａｃｔｏｒ,ｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄａｎｄａｐｐｒｏｘｉｍａｔｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄａｓｓｏｃｉａｔｅｄｗｉｔｈｄｙｎａｍｉｃａｌｓｙｓ…     

The asymptotic theory of initial value problems for semilinear pertubed wave equations in two space dimensions

The asymptotic theory of initial value problems for semilinear ware equations in two space dimensions was dealt with. The well-posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a special wave equation in two space dimensions. Foundation item: Sichuan Youth Foundation (1999-09) Biography: LAI Shao-yong (1965−), Associate Professor     

The numbers of jump layers of boundary value problems in quasilinear differential equations

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1] is always equal to zero.     

Eigenfunction expansion method of upper triangular operator matrix and application to two-dimensional elasticity problems based on stress formulation

This paper studies the eigenfunction expansion method to solve the two-dimensional(2D) elasticity problems based on the stress formulation.The fundamentalsystem of partial differential equations of the 2D problems is rewritten as an upper tri-angular differential system based on the known results,and then the associated uppertriangular operator matrix matrix is obtained.By further research,the two simpler com-plete orthogonal systems of eigenfunctions in some space are obtained,which belong tothe two block operators arising in the operator matrix.Then,a more simple and conve-nient general solution to the 2D problem is given by the eigenfunction expansion method.Furthermore,the boundary conditions for the 2D problem,which can be solved by thismethod,are indicated.Finally,the validity of the obtained results is verified by a specificexample.     

On the reduction of some second-order nonlinear ODEs in physics and mechanics to first-order nonlinear integrodifferential and Abel’s classes of equations

Second-order ordinary differential equations (ODEs) with strong nonlinear stiffness terms (cubic nonlinearities) governing wave motions, dynamic crack propagations, nonlinear oscillations etc. in physics and nonlinear mechanics are analyzed. Selecting as guide line a second-order nonlinear ODE of the form of the forced Duffing equation and using admissible functional transformations it is possible to reduce it to an equivalent first-order nonlinear integrodifferential equation. The reduced equation is exact. In the limits of small or large values of the parameter characterizing this nonlinear problem, it is shown that further reductions lead to a nonlinear ODE of the Abel classes. Taking into account the known exact analytic solutions of this equivalent equation it is proved that there does not exist an exact analytic solution of this type of equations. However, in cases when convenient functional relations connecting all parameters of the corresponding null equation and the characteristics of the driving force exist, approximate analytic solutions to the problem under consideration are provided.