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1.
Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether's theorem is used to determine the extended conservation laws of the original equations. Finally, as the application of the method, the conservation laws of Drinfel'd-Sokolov-Wilson equation and Benjamin-Bona-Mahony equation are constructed.  相似文献   

2.
ZHANGYi 《理论物理通讯》2004,42(6):899-902
A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results.  相似文献   

3.
We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.  相似文献   

4.
ZHANGYi 《理论物理通讯》2004,42(5):669-671
A geometrical approach to the Hojman theorem of a rotational relativistic Birkhoffian system is presented.The differential equations of motion of the system are established. According to the invariance of differential equations under infinitesimal transformation, the determining equations of Lie symmetry are constructed. A new conservation law of the system, called Hojman theorem, is obtained, which is the generalization of previous results given sequentially by Hojman, Zhang, and Luo et al. In terms of the theory of modern differential geometry a proof of the theorem is given.  相似文献   

5.
This paper extends Hojman’s conservation law to the third-order differential equation.A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion.The generators contain variations of the time and generalized coordinates.Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained.A simple example is presented to illustrate the applications of the results.  相似文献   

6.
赵娟  罗一 《中国物理 B》2011,20(4):43402-043402
Based on an extended London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES),the Ba + HF reaction has been studied by the quasi-classical trajectory (QCT) method. The reaction integral cross section as a function of collision energy for the Ba + HF → BaF + H reaction is presented and the influence of isotope substitution on the differential cross sections (DCSs) and alignments of the product’s rotational angular momentum have also been studied. The results suggest that the integral cross sections increase with increasing collision energy,and the vibrational excitation of the reagent has great influence on the DCS. In addition,the product’s rotational polarization is very strong as a result of heavy-heavy-light (HHL) mass combination,and the distinct effect of isotope substitution on the stereodynamics is also revealed.  相似文献   

7.
ZHANG Yi 《理论物理通讯》2008,50(10):851-854
For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.  相似文献   

8.
Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman‘s conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.  相似文献   

9.
Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman‘s conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.  相似文献   

10.
The reaction of pp → pK^+A is a very good channel to study N^* resonances through their KA decay mode, because there is no mixing of isospin I = 1/2 and I = 3/2 due to isospin conservation. In this work, we extend a resonance model, which can reproduce the total cross section very well, to offer differential cross section information about this reaction. It can serve as a reference to build the scheduled hadron detector at Lanzhou Cooler Storage Ring (CSR). Experiment measurement of these differential cross sections in the future will supply us more constraints on the model and help us understanding the strangeness production dynamics better.  相似文献   

11.
This paper employed the principle of undetermined coefficients and Bernoulli sub-ODE methods to acquire the topological, non-topological, periodic wave and algebraic solutions of the coupled generalized Schrödinger–Boussinesq system (CGSBs). The concept of Lie point symmetry is applied to derive the point symmetries of the CSGE. The problem on nonlinear self-adjointness of the CSGE has not been solved in previous time. In the present paper, we solve this problem and find an explicit form of the differential substitution providing the nonlinear self-adjointness. Then we use this fact to construct a set of conserved vectors using the classical symmetries admitted by the equation and the general conservation laws (Cls) theorem presented by Ibragimov. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.  相似文献   

12.
The fundamental relation between Lie-Bäcklund symmetry generators andconservation laws of an arbitrary differential equation is derived without regardto a Lagrangian formulation of the differential equation. This relation is used inthe construction of conservation laws for partial differential equations irrespectiveof the knowledge or existence of a Lagrangian. The relation enables one toassociate symmetries to a given conservation law of a differential equation.Applications of these results are illustrated for a range of examples.  相似文献   

13.
The purpose of this paper is to establish a group theoretical foundation of conservation theorems for arbitrary systems of partial differential equations. It is shown that any conservation law for differential equations is derivable from the invariance properties of the equations with respect to a group of Lei-Bäcklund tangent transformations.  相似文献   

14.
Abstract

A fully nonlinear family of evolution equations is classified. Nine new integrable equations are found, and all of them admit a differential substitution into the Korteweg-de Vries or Krichever-Novikov equations. One of the equations contains hyperelliptic functions, but it is transformable into the Krichever-Novikov equation by a differential substitution that only involves elliptic functions.  相似文献   

15.
The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter.  相似文献   

16.
凌寅生  姜莉 《大学物理》1998,17(11):8-10
应用初等微分法,导出经典力学中Noether定理公式,该定理除可用以求出常见的动量守恒与能量守恒等定律以外,尚可讨论含时系统的对称性与守恒定律。  相似文献   

17.
In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H (x)utt.  相似文献   

18.
郝世峰  崔晓鹏 《物理学报》2012,61(3):39204-039204
质量守恒是平流扩散差分方程所必须满足的基本性质,但是由于差分格式不具有正定性(positive-definite),因此在积分过程中负质量的产生会导致总质量不守恒.针对这一问题,本文从负质量产生的物理意义出发,提出了一个简单有效的新正定性重整化方案,通过点源平流扩散试验表明,该方案不但解决了平流扩散差分方程的正定性问题,同时保证了总质量守恒性.与WRF模式中采用的"重整化方案"相比,具有物理含义清楚、并且简单易行的优点.  相似文献   

19.
张毅 《物理学报》2004,53(12):4026-4028
研究了Birkhoff系统的Hojman定理的几何基础.建立了系统的运动微分方程和Hojman守恒 定理,利用现代微分几何给出了Birkhoff系统的Hojman定理的一个证明. 关键词: Birkhoff系统 Hojman定理 对称性 微分几何  相似文献   

20.
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.  相似文献   

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