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1.
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
2.
The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献
3.
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
4.
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
5.
ZHANG Shun-Li ZHU Xiao-Ning WANG Yong-Mao LOU Sen-Yue 《理论物理通讯》2008,49(4):829-832
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations. 相似文献
6.
The symmetry reduction method based on the Fr′echet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献
7.
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
8.
Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential
evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution
equations were lifted to the corresponding functional partial differential equations in functional space by introducing the
time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The
algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact
analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution
equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer
numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic
dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution
equations both analytically and numerically.
Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program
Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China 相似文献
9.
Double-wave solutions and Lie symmetry analysis to the (2 + 1)-dimensional coupled Burgers equations
This paper investigates the (2 + 1)-dimensional coupled Burgers equations (CBEs) which is an important nonlinear physical model. In this respect, by making use of the generalized unified method (GUM), a series of double-wave solutions of the (2 + 1)-dimensional coupled Burgers equations are derived. The Lie symmetry technique (LST) is also utilized for the symmetry reductions of the (2 + 1)-dimensional coupled Burgers equations and extracting a non-traveling wave solution. Through some figures, we discussed the wave structures of the double-wave solutions of the CBEs for different values of parameters in these solutions. 相似文献
10.
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
11.
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic
potential vorticity equation
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By means of the reductive perturbation method, three types
of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP)
equations are derived from the baroclinic potential vorticity (BPV)
equation, including the modified KP (mKP) equation, standard KP equation
and cylindrical KP (cKP) equation. Then some solutions of
generalized cKP and KP equations with certain conditions are given
directly and a relationship between the generalized mKP equation and
the mKP equation is established by the symmetry group direct method
proposed by Lou et al. From the relationship and the solutions
of the mKP equation, some solutions of the generalized mKP equation can be
obtained. Furthermore, some approximate solutions of the baroclinic
potential vorticity equation are derived from three types of
generalized KP equations. 相似文献
12.
Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration
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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
13.
In this paper, the symmetry group of the (2+1)-dimensional Painlev? integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations. 相似文献
14.
LIU Hong-Zhun PAN Zu-Liang 《理论物理通讯》2005,44(7)
By a known transformation, (2 1)-dimensional Brioer-Kaup equations are turned to a single equation.The classical Lie symmetry analysis and similarity reductions axe performed for this single equation. From some of reduction equations, new exact solutions are obtained, which contain previous results, and more exact solutions can be created directly by abundant known solutions of the Burgers equations and the heat equations. 相似文献
15.
LIUHong-Zhun PANZu-Liang 《理论物理通讯》2005,44(1):15-18
By a known transformation, (2 1)-dimensional Brioer Kaup equations are turned to a single equation.The classical Lie symmetry analysis and similarity reductions are performed for this single equation. From some of reduction equations, new exact solutions are obtained, which contain previous results, and more exact solutions can be created directly by abundant known solutions of the Burgers equations and the heat equations. 相似文献
16.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 相似文献
17.
A new method is used to determine the nonclassical potential symmetry generators of Burgers equation.Some classes of new explicit solutions, which cannot be obtained by Lie symmetry group of Burgers equation or its integrated equation, are obtained by using these new nonclassical potential symmetry generators. 相似文献
18.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 相似文献
19.
对称性分析是自然科学研究中的重要方法之一. 利用对称性分析研究了一个描述两层流体体系的模型即耦合Burgers方程的对称性. 利用对称性给出了这个模型的四种对称性约化并给出了这些约化方程的一些特殊的严格解,如有理解、行波孤立子解和非行波孤立子解.
关键词:
对称性约化
耦合Burgers方程
孤立子 相似文献
20.
QINMao-Chang MEIFeng-Xiang XUXue-Jun 《理论物理通讯》2005,44(1):11-14
A new method is used to determine the nonclassical potential symmetry generators of Burgers equation.Some classes of new explicit solutions, which cannot be obtained by Lie symmetry group of Burgers equation or its integrated equation, are obtained by using these new nonclassical potential symmetry generators. 相似文献