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1.
Finite symmetry transformation group of the Konopelchenkoben Dubrovsky equation from its Lax pair 下载免费PDF全文
Starting from a weak Lax pair, the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method. And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type. Furthermore, a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution. 相似文献
2.
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
3.
In this paper,the problem of determining the most general Lie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation(HSE) is analyzed.By applying the basic Lie symmetry method for the HSE,the classical Lie point symmetry operators are obtained.Also,the algebraic structure of the Lie algebra of symmetries is discussed and an optimal system of onedimensional subalgebras of the HSE symmetry algebra which creates the preliminary classification of group invariant solutions is constructed.Particularly,the Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained.Mainly,the conservation laws of the HSE are computed via three different methods including Boyer's generalization of Noether's theorem,first homotopy method and second homotopy method. 相似文献
4.
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2 1)-dimensional variable coefficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation. 相似文献
5.
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2007,48(3):405-410
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation. 相似文献
6.
Based on the general direct method developed by Lou et al. [J. Phys. A: Math. Gen. 38 (2005) L129], the symmetry group theorem is obtained,from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenko-Dubrovsky (KD) equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution. 相似文献
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8.
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic
potential vorticity equation 下载免费PDF全文
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
9.
SU(2) andSU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
Constantin Brif 《International Journal of Theoretical Physics》1997,36(7):1651-1682
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of
the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated
with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent
states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset
of algebra eigenstates. We develop the general formalism and apply it to theSU(2) andSU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in both cases by a method that employs
analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions
for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states
and intelligent states are examined and relations between them are studied by using their analytic representations. 相似文献
10.
《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
11.
研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.
关键词:
Appell方程
Chetaev 型约束力学系统
Lie对称性
守恒量 相似文献
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In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. 相似文献
15.
MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(12)
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik-Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only special cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
16.
MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(6):1005-1010
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
17.
In this paper, a detailed Lie symmetry analysis of the (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method, which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. 相似文献
18.
Based on some known facts of integrable models, this paper proposes a new (2+1)-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied 相似文献
19.
Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation 下载免费PDF全文
<正>This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+l)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method.Its symmetry algebra, symmetry group and group-invariant solutions are analysed.Otherwise,some exact explicit solutions are obtained from the corresponding(2+1)-dimensional equation,the inviscid barotropic nondivergent vorticy equation.To show the properties and characters of these solutions,some plots as well as their possible physical meanings of the atmospheric circulation are given. 相似文献
20.
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