共查询到16条相似文献,搜索用时 515 毫秒
1.
Symmetries and conservation laws of one Blaszak-Marciniak four-field lattice equation*Symmetries and conservation laws of one Blaszak-Marciniak four-field lattice equation*Symmetries and conservation laws of one Blaszak-Marciniak four-field lattice equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper, by using the classical Lie symmetry approach, Lie point symmetries and reductions of one Blaszak- Marciniak (BM) four-field lattice equation are obtained. Two kinds of exact solutions of a rational form and an exponential form are given. Moreover, we show that the equation has a sequence of generalized symmetries and conservation laws of polynomial form, which further confirms the integrability of the BM system. 相似文献
2.
Form Invariance and Lie Symmetries of the Rotational Relativistic Birkhoff System 总被引:2,自引:0,他引:2
下载免费PDF全文
![点击此处可从《中国物理快报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
For a rotational relativistic Birkhoff system,the relation between the form invariance and the Lie symmetries are given Under infinitesimal transformations of groups.If the infinitesimal transformation generators ξ0 and ξμ satisfy the conditions of the form invariance,and the determining equation of Lie symmetries holds,the form invariance leads to a Lie symmetry of the system.Furthermore,if the infinitesimal transformations generators ξ0 and ξμ satisfy the conditions of the form invariance and the determining equation of Lie symmetry holds,and if there is a gauge function G satisfying the structure equation of Lie symmetry,then the form invariance will lead to the Lie symmetrical conserved quantity of the system.An example is given to illustrate the application of the results. 相似文献
3.
We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained. 相似文献
4.
After a Birkhoff system is restricted by constraints, the determining equations, the Lie symmetries, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some Lie symmetries will disappear and under certain conditions some Lie symmetries will still remain present. The condition under which Lie symmetries and conserved quantities of the system will remain is given. 相似文献
5.
The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result. 相似文献
6.
Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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.
Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
8.
XIA Li-Li LI Yuan-Cheng WANG Xian-Jun 《理论物理通讯》2009,51(6):1073-1077
The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results. 相似文献
9.
The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation. 相似文献
10.
Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Based on the invariance of differential equations under
infinitesimal transformations of group, Lie symmetries, exact
invariants, perturbation to the symmetries and adiabatic invariants
in form of non-Noether for a Lagrange system are presented. Firstly,
the exact invariants of generalized Hojman type led directly by Lie
symmetries for a Lagrange system without perturbations are given.
Then, on the basis of the concepts of Lie symmetries and higher
order adiabatic invariants of a mechanical system, the perturbation
of Lie symmetries for the system with the action of small
disturbance is investigated, the adiabatic invariants of generalized
Hojman type for the system are directly obtained, the conditions for
existence of the adiabatic invariants and their forms are proved.
Finally an example is presented to illustrate these results. 相似文献
11.
EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS 总被引:1,自引:0,他引:1
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain. 相似文献
12.
13.
EFFECTS OF NON-CONSERVATIVE FORCES ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF A LAGRANGE SYSTEM 总被引:1,自引:0,他引:1
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Non-conservative forces are exerted on a Lagrange system. Their effects on Lie symmetries, structure equation and conserved quantities of the system are studied. It can be seen that some Lie symmetries disappear and some new Lie symmetries emerge. Under certain conditions, some Lie symmetries will still remain present. 相似文献
14.
Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split
system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex
heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie
symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the
complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute
a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed
by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial
differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential
equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition
that gives the criteria when the Lie-like operators are symmetries of the split system. 相似文献
15.
把极角θ视为独立变量,得到Kepler系统的轨道微分方程.首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量。 相似文献
16.
To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34) equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant so... 相似文献