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1.
The complete discrimination system for polynomial method is applied to the long-short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the (G~/G)-expansion method, we gain some new solutions. 相似文献
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We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics. 相似文献
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Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results. 相似文献
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Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration 下载免费PDF全文
The Lie symmetries and conserved quantities of a
two-dimensional nonlinear diffusion equation of concentration are
considered. Based on the invariance of the two-dimensional nonlinear
diffusion equation of concentration under the infinitesimal
transformation with respect to the generalized coordinates and time,
the determining equations of Lie symmetries are presented. The Lie
groups of transformation and infinitesimal generators of this
equation are obtained. The conserved quantities associated with the
nonlinear diffusion equation of concentration are derived by
integrating the characteristic equations. Also, the solutions of the
two-dimensional nonlinear diffusion equation of concentration can be
obtained. 相似文献
6.
Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration 下载免费PDF全文
The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained. 相似文献
7.
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper. 相似文献
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Swapna Roy A. Roy Chowdhury Mrityunjoy De 《International Journal of Theoretical Physics》1988,27(1):47-55
It is demonstrated that Lie point symmetries associated with a nonlinear equation for short waves in three dimensions generate an infinite-dimensional Lie algebra—a loop Algebra. Classification of the independent sets of the subalgebra is done through the adjoint action of the corresponding generators. Different forms of similarity solutions are discussed. 相似文献
12.
Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results. 相似文献
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This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results. 相似文献
14.
Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices 下载免费PDF全文
The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results. 相似文献
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In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. 相似文献
16.
The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems 下载免费PDF全文
This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results. 相似文献
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Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices 下载免费PDF全文
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This
approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone. 相似文献
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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 相似文献
19.
The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field 下载免费PDF全文
In this paper, a constant of motion of charged particle motion in
homogeneous electromagnetic field is derived from Newton's equations and the
characteristics of partial differential equation, the related
Lagrangian is also given by means of the obtained constant of motion. By
discussing the Lie symmetry for this classical system, this paper
obtains the general
expression of the conserved quantity. It is shown that the conserved
quantity is the same as the constant of motion in essence. 相似文献
20.
Lie symmetries and conserved quantities of non—holonomic mechanical systems with unilateral Vacco constraints 总被引:5,自引:0,他引:5 下载免费PDF全文
In this paper,we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints.we give the conditions and the form of conserved quantities due to the Lie symmetries of the systems,and present the inverse problem of the above proble,i.e.finding the corresponding Lie symmetry transformation according to a given integral of the system.Finally,we give an example to illustrate the application of the results. 相似文献