共查询到20条相似文献,搜索用时 15 毫秒
1.
LINJi LOUSen-Yue 《理论物理通讯》2002,37(3):265-268
Using the standard truncated Painleve analysis,we can obtain a Backlund transformation of the (3 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation and get some(3 1)-dimensional single-,two- and three-soliton solutions and some new types of multisoliton solutions of the (3 1)-dimensional NNV system from the Backlund transformation and the trivial vacuum solution. 相似文献
2.
Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik-Novikov-Veselov equation
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We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions. 相似文献
3.
Compacton, Peakon, and Foldon Structures in the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation 总被引:1,自引:0,他引:1
By the use of the extended homogenous
balance method, the Backlund transformation
for a (2+1)-dimensional integrable model, the(2+1)-dimensional
Nizhnik-Novikov-Veselov (NNV) equation, is obtained,
and then the NNV equation is transformed into three
equations of linear, bilinear, and tri-linear forms,
respectively. From the above three equations,
a rather general variable separation solution
of the model is obtained. Three novel class localized structures
of the model are founded by the entrance of two variable-separated
arbitrary functions. 相似文献
4.
Using Jacobi elliptic function linear superposition approach for
the (1+1)-dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK)
equation and the (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV)
equation, many new periodic travelling wave solutions with
different periods and velocities are obtained based on the known
periodic solutions. This procedure is crucially dependent on a
sequence of cyclic identities involving Jacobi elliptic functions
sn(ξ,m), cn(ξ,m), and dn(ξ,m). 相似文献
5.
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions. 相似文献
6.
Higher-Dimensional KdV Equations and Their Soliton Solutions 总被引:2,自引:0,他引:2
A (2+1)-dimensional KdV equation is obtained by use of Hirota
method, which possesses N-soliton solution, specially its exact
two-soliton solution is presented. By employing a proper algebraic
transformation and the Riccati equation, a type of bell-shape
soliton solutions are produced via regarding the variable in the
Riccati equation as the independent variable. Finally, we extend
the above (2+1)-dimensional KdV equation into (3+1)-dimensional
equation, the two-soliton solutions are given. 相似文献
7.
By means of the generalized direct method, a relationship is
constructed between the new solutions and the old ones of the
(3+1)-dimensional breaking soliton equation. Based on the
relationship, a new solution is obtained by using a given
solution of the equation. The symmetry is also obtained for the
(3+1)-dimensional breaking soliton equation. By using the equivalent
vector of the symmetry, we construct a seven-dimensional symmetry
algebra and get the optimal system of group-invariant solutions. To
every case of the optimal system, the (3+1)-dimensional breaking
soliton equation is reduced and some solutions to the reduced
equations are obtained. Furthermore, some new explicit solutions are
found for the (3+1)-dimensional breaking soliton equation. 相似文献
8.
A Bilinear Backlund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation
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Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation. As an application, soliton solution and stationary rational solution for the (3+1)- dimensional soliton equation are presented. 相似文献
9.
With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the (2+1)-dimensional Nizhnik-Novikov-Veselov system (NNV) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the (2+1)-dimensional NNV system. 相似文献
10.
Based on the extended mapping deformation method and symbolic
computation, many exact travelling wave solutions are found for
the (3+1)-dimensional JM equation and the (3+1)-dimensional KP
equation. The obtained solutions include solitary solution, periodic wave solution,
rational travelling wave solution, and Jacobian and Weierstrass
function solution, etc. 相似文献
11.
In this paper, the fractional-order model is used to study dust acoustic rogue waves in dusty plasma. Firstly, based on control equations, the multi-scale analysis and reduced perturbation method are used to derive the (3+1)-dimensional modified Kadomtsev-Petviashvili (MKP) equation. Secondly, using the semi-inverse method and the fractional variation principle, the (3+1)-dimensional time-fractional modified Kadomtsev-Petviashvili (TF-MKP) equation is derived. Then, the Riemann-Liouville fractional derivative is used to study the symmetric property and conservation laws of the (3+1)-dimensional TF-MKP equation. Finally, the exact solution of the (3+1)-dimensional TF-MKP equation is obtained by using fractional order transformations and the definition and properties of Bell polynomials. Based on the obtained solution, we analyze and discuss dust acoustic rogue waves in dusty plasma. 相似文献
12.
In this paper, the investigation is focused on a (3+1)-dimensional variable-coefficient Kadomtsev- Petviashvili (vcKP) equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the (3+1)-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the (3+1)-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant. 相似文献
13.
Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case,
the solitary wave solution to NNV equation are also obtained. 相似文献
14.
LINJi QIANXian-Ming 《理论物理通讯》2003,40(3):259-261
Using the (2 1)-dimensional Schwartz dcrivative, the usual (2 1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n 1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3 1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3 1)-dimensional equation are obtained. 相似文献
15.
A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献
16.
BAICheng-Lin LIUXi-Qiang ZHAOHong 《理论物理通讯》2004,42(6):827-830
We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolution equation. We take the (3 1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions. 相似文献
17.
B?cklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation
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We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions. 相似文献
18.
We generalize the ■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero. 相似文献
19.
The (2+1)-dimensional Konopelchenko-Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko-Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko-Dubrovsky equation. 相似文献
20.
In this paper, we introduce
the notion of a (2+1)-dimensional differential equation describing
three-dimensional hyperbolic spaces (3-h.s.). The (2+1)-dimensional coupled nonlinear Schrödinger equation and its
sister equation, the (2+1)-dimensional coupled derivative nonlinear Schrödinger equation, are shown to describe 3-h.s. The (2+1)-dimensional generalized HF model:
St={(1/2i)[S,Sy]+2iσS}x,
σx=-(1/4i)tr(SSxSy), in which S∈[GLC(2)]/[GLC(1)×GLC(1)], provides another example of (2+1)-dimensional differential equations describing 3-h.s. As a direct consequence, the geometric construction of an infinite
number of conservation laws of such equations is illustrated.
Furthermore we display a new infinite number of conservation laws
of the (2+1)-dimensional nonlinear Schrödinger equation and the
(2+1)-dimensional derivative nonlinear Schrödinger equation
by a geometric way. 相似文献