共查询到18条相似文献,搜索用时 93 毫秒
1.
Finite symmetry transformation group and localized structures of the (2+1)-dimensional coupled Burgers equation 下载免费PDF全文
In this paper, the finite symmetry transformation group of the (2+1)-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the (2+1)-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures. 相似文献
2.
A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation 下载免费PDF全文
Recently the (G'/G)-expansion
method was proposed to find the traveling wave solutions of
nonlinear evolution equations. This paper shows that the
(G'/G)-expansion method is a special form of the truncated
Painlevé expansion method by introducing an intermediate
expansion method. Then the generalized
(G'/G)--(G'/G) expansion method is naturally
derived from the standpoint of the nonstandard truncated
Painlevé expansion. The application of the generalized method to
the mKdV equation shows that it extends the range of exact solutions
obtained by using the (G'/G)-expansion
method. 相似文献
3.
Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation 下载免费PDF全文
In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found. 相似文献
4.
A connection between the (G′/G)-expansion method and the truncated Painlev 'e expansion method and its application to the mKdV equation 下载免费PDF全文
Recently the (G′/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G′/G)-expansion method is a special form of the truncated Painlev'e expansion method by introducing an intermediate expansion method. Then the generalized (G′/G)-(G/G′) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev'e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the ( G′/ G)-expansion method. 相似文献
5.
Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation 下载免费PDF全文
This paper is concerned with the generalized variable-coefficient nonlinear evolution equation(vc-NLEE).The complete integrability classification is presented,and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlev′e analysis.Then,the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method,and the Lax pairs(LP) of the vc-NLEEs are constructed in terms of the integrable conditions. 相似文献
6.
The residual symmetry of the generalized Kaup-Kupershmidt(gKK) equation is obtained from the truncated Painlevé expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Furthermore, the g KK equation is proved to integrable in the sense of owning consistent Riccati expansion and some new B¨acklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given. 相似文献
7.
The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants. 相似文献
8.
《理论物理通讯》2015,(8)
Using the standard truncated Painlev expansion, the residual symmetry of the(2+1)-dimensional modified dispersive water-wave system is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived by utilizing the obtained symmetries. The symmetries of the system are also derived through the Clarkson-Kruskal direct method, and several types of explicit reduction solutions relate to the trigonometric or the hyperbolic functions are obtained. Finally, some special solitons are depicted from one of the solutions. 相似文献
9.
《理论物理通讯》2017,(8)
Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system. 相似文献
10.
Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms 下载免费PDF全文
The complete band gaps (CBGs) of shallow water waves
propagating over bottoms with periodically drilled holes are
investigated numerically by the plane wave expansion method. Four
different patterns are considered, containing triangular, square,
hexagonal and circular cross-sectioned holes arranged into
triangular lattices. Results show that the width of CBGs can be
changed by adjusting the orientation of noncircular holes and the
effect of hole shape on the width of the maximal CBGs is discussed. 相似文献
11.
12.
The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. 相似文献
13.
ZHANG Chun-Yi GAO Yi-Tian XU Tao LI Li-Li SUN Fu-Wei LI Juan MENG Xiang-Hua WEI Guang-Mei 《理论物理通讯》2008,49(3):673-678
In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified. 相似文献
14.
PENG Yan-Ze 《理论物理通讯》2004,41(5):669-670
A new multisoliton solution to the
(2+1)-dimensional KdV equation is obtained by means of the
truncated Painleve expansion method and a direct ansatz technique.
This new exact solution is periodic in the propagating direction
x and exponentially decaying in y and thus it is called
periodic solitons. A typical spatial structure of it is
illustrated by the figures. 相似文献
15.
Through Pickering's and extended
Painlevé nonstandard truncated
expansion method, this paper solves the phase-separating dynamics
equation of diblock copolymer, and obtains various exact solutions.
We discuss non-complex special solutions which can be made up of
hyperbolic functions or elliptic functions. 相似文献
16.
Residual symmetry,interaction solutions,and conservation laws of the(2+1)-dimensional dispersive long-wave system 下载免费PDF全文
We explore the(2+1)-dimensional dispersive long-wave(DLW) system. From the standard truncated Painlev′e expansion, the B¨acklund transformation(BT) and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the(2+1)-dimensional DLW system is consistent Riccati expansion(CRE) solvable. If the special form of(CRE)-consistent tanh-function expansion(CTE) is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem. 相似文献
17.
A generalized Kadomtsev-Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev-Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev-Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. 相似文献
18.
截断光束的二阶矩矩阵 总被引:1,自引:0,他引:1
采用复高斯展开法和维格纳分布函数(WDF),推导出了截断光束的二阶矩矩阵通过大气湍流的传输公式。研究表明,将硬边光阑的复高斯展开函数引入z=0平面处的WDF中,能够避免截断光束二阶矩的积分发散问题,得到z=0平面处二阶矩的解析结果,并且保证了精度,从而方便地得到截断光束在大气湍流中传输的二阶矩矩阵。实验所得到的结果具有一般性,即无截断光束的二阶矩矩阵通过大气湍流传输和截断光束的二阶矩矩阵在自由空间的传输都可以分别作为特例给出。 相似文献