共查询到20条相似文献,搜索用时 31 毫秒
1.
JI Li-Na QU Chang-Zheng 《理论物理通讯》2006,46(10)
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained. 相似文献
2.
QU ChangZheng 《理论物理通讯》1999,31(4):581-588
The generalized conditional symmetry method, which is a generalization of the conditional symmetry method, is used to study the nonlinear diffusion-convection-reaction equations. In particular, power law and exponential diffusivities are examined and we derive mathematical forms of the convection and reaction terms which permit a new type of generalized conditional symmetry. Some new exact solutions of the governing equations can be obtained by solving the systems of two or three ordinary differential equations which arise from the compatibility of the generalized conditional symmetries and the governing equations. 相似文献
3.
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations (ODEs). We classify a class of fourth-order evolution equations which admit certain
higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is
something essential for the dimensional reduction of evolution equations. 相似文献
4.
The functionally generalized variable separation solutions of a general KdV-type equations ut=uxxx + A(u, ux)uxx + B(u, ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations. 相似文献
5.
Conditional Symmetry Groups of Nonlinear Diffusion Equations with x-Dependent Convection and Absorption 总被引:1,自引:0,他引:1
The generalized
conditional symmetry and sign-invariant approaches are developed
to study the nonlinear diffusion equations with x-dependent
convection and source terms. We obtain conditions under which the
equations admit the second-order generalized conditional
symmetries and the first-order sign-invariants on the solutions.
Several types of different generalized conditional symmetries and
first-order sign-invariants for the equations with diffusion of
power law are obtained. Exact
solutions to the resulting equations are constructed. 相似文献
6.
ZHANG Shun-Li WANG Yong LOU Sen-Yue 《理论物理通讯》2007,47(6):975-980
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples. 相似文献
7.
Using the generalized conditional symmetry approach, a complete list of canonicalforms for the Kortewegde-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained.The exact DDFSSs of the resulting equations are explicitly exhibited. 相似文献
8.
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditional symmetries (GCSs) is implemented. The reducibility of the initial-value problem for an evolution equation to a Cauchy problem for a system ofordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry. Complete classification theorems are obtained and some examples are taken to show the main reduction procedure. 相似文献
9.
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
10.
Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations 总被引:1,自引:0,他引:1
ZHANG Shun-Li LOU Sen-Yue QU Chang-Zheng YUE Rui-Hong 《理论物理通讯》2005,44(4):589-596
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
11.
12.
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. 相似文献
13.
LI Ji-Na ZHANG Shun-Li ZUO Su-Li 《理论物理通讯》2008,49(3):545-548
We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations. We characterize these equations that admit certain higherorder GCSs and show the main reduction procedure by some examples. The obtained reductions cannot be derived within the framework of the standard Lie approach. 相似文献
14.
Lina Ji 《Physica A》2010,389(24):5655-5661
The second-order conditional Lie-Bäcklund symmetries of nonlinear diffusion equations with variable coefficients are studied. A number of examples are considered and some exact solutions are constructed via the compatibility of conditional Lie-Bäcklund symmetries and the governing equations. These solutions possess the extended forms of the separation of variables, including the extensions of the instantaneous source solutions of the porous medium equations. 相似文献
15.
This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations.By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions (FSSs) and construct some exact FSSs to the resulting equations. 相似文献
16.
The functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations are studied by applying the conditional Lie–Bäcklund symmetry method. A complete list of canonical forms for such equations are presented. Exact solutions to the resulting equations are constructed. The asymptotic behaviors and blow-up properties of some solutions are also discussed. 相似文献
17.
Lina Ji 《Physica A》2012
This paper considers conditional Lie–Bäcklund symmetries of the radially symmetric nonlinear diffusion equations with source. We obtain a complete list of canonical forms for such equations which admit higher-order conditional symmetries. As a consequence, the solutions of the resulting equations are constructed on the invariant subspaces admitted by the corresponding equations. 相似文献
18.
ZHANG Shun-Li 《理论物理通讯》2006,45(6):969-978
The generalized conditional symmetry is developed to study the variable
separation for equations of type uxt=A(u,ux)uxx+B(u,ux). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their
exact separable solutions are constructed. 相似文献
19.
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries (GCSs). Complete group classification results are presented, and some examples are given to show the main reduction procedure. 相似文献
20.
《Journal of Nonlinear Mathematical Physics》2013,20(4):431-441
In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi's method. 相似文献