共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlev′e method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems.The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion(CTE) method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system. 相似文献
3.
The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr?dinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method. 相似文献
4.
In this paper, Lie symmetry is investigated for a new integrable
coupled Korteweg--de Vries (KdV) equation system. Using some symmetry
subalgebra of the equation system, we obtain five types of the
significant similarity reductions. Abundant solutions of the coupled
KdV equation system, such as the solitary wave solution, exponential
solution, rational solution and polynomial solution, etc. are
obtained from the reduced equations. Especially, one type of
group-invariant solution of reduced equations can be acquired by
means of the Painlev\'e I transcendent function. 相似文献
5.
The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV(BSmKdV)equation admits Painlevé property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems. 相似文献
6.
In this paper, the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given, and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained. 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.
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
9.
From the point of view of approximate symmetry, the modified
Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak
dissipation is investigated. The symmetry of a system of the
corresponding partial differential equations which approximate the
perturbed mKdV--Burgers equation is constructed and the
corresponding general approximate symmetry reduction is derived;
thereby infinite series solutions and general formulae can be
obtained. The obtained result shows that the zero-order similarity
solution to the mKdV--Burgers equation satisfies the Painlevé II
equation. Also, at the level of travelling wave reduction, the
general solution formulae are given for any travelling wave solution
of an unperturbed mKdV equation. As an illustrative example, when
the zero-order tanh profile solution is chosen as an initial
approximate solution, physically approximate similarity solutions
are obtained recursively under the appropriate choice of parameters
occurring during computation. 相似文献
10.
LIU Ping LOU Sen-Yue 《理论物理通讯》2009,51(1):27-34
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries. 相似文献
11.
《理论物理通讯》2017,(5)
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method.The auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. 相似文献
12.
Lie group analysis,numerical and non-traveling wave solutions for the (2+l)-dimensional diffusion-advection equation with variable coefficients 下载免费PDF全文
In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (Gl/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions. 相似文献
13.
New explicit exact solutions for a generalized Hirota—Satsuma coupled KdV system and a coupled MKdV equation 总被引:7,自引:0,他引:7 下载免费PDF全文
In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained. 相似文献
14.
Most of the nonlinear physics systems are essentially nonintegrable.There in no very doog analytical approach to solve nonintegrable system.The variable separation approach is a powerful method in linear physics.In this letter,the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation.The method is valid not only for integrable models but also for nonintegrable models.Taking a nonintegrable coupled KdV equation system as a simple example,abundant solitary wave solutions and conoid wave solutions are revealed. 相似文献
15.
The extended symmetry approach is used to study the
general Korteweg-de Vries-type (KdV-type) equation. Several
variable-coefficient equations are obtained. The solutions of
these resulting equations can be constructed by the solutions of
original models if their solutions are well known, such as the
standard constant coefficient KdV equation and the standard compound
KdV--Burgers equation, and so on. Then any one of these
variable-coefficient equations can be considered as an original
model to obtain new variable-coefficient equations whose solutions
can also be known by means of transformation relations between
solutions of the resulting new variable-coefficient equations and the
original equation. 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
17.
YAO Ruo-Xia JIAO Xiao-Yu LOU Sen-Yue 《理论物理通讯》2009,51(5):785-788
Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky (KS) equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here. 相似文献
18.
Starting from the truncated Painlev′e expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries(AB-mKdV) equation is derived. The residual symmetry is localized and the AB-mKdV equation is transformed into an enlarged system by introducing one new variable. Based on Lie's first theorem, the finite transformation is obtained from the localized residual symmetry. Further, considering the linear superposition of multiple residual symmetries gives rises to N-th B?cklund transformation in the form of the determinant. Moreover, the P_sT_d(the shifted parity and delayed time reversal) symmetric exact solutions(including invariant solution, breaking solution and breaking interaction solution) of AB-mKdV equation are presented and two classes of interaction solutions are depicted by using the particular functions with numerical simulation. 相似文献
19.
In this paper, new explicit and exact travelling wave solutions for a compound KdV-Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV-Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations. 相似文献
20.
《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