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1.
We show that higher-dimensional integrable systems including the
(2+1)-dimensional generalized sine-Gordon equation and the
(2+1)-dimensional complex mKdV equation are associated with motions of
surfaces induced by endowing with an extra space variable to the
motions of curves on S2(R) and S3(R). 相似文献
2.
On High-Frequency Soliton Solutions to a (2+1)-Dimensional Nonlinear Partial Differential Evolution Equation 下载免费PDF全文
Kuetche Kamgang Victor Bouetou Bouetou Thomas Timoleon Crepin Kofane 《中国物理快报》2008,25(2):425-428
A (2+1)-dimensional nonlinear partial differential evolution (NLPDE) equation is presented as a model equation for relaxing high-rate processes in active barothropic media. With the aid of symbolic computation and Hirota's method, some typical solitary wave solutions to this (2+1)-dimensional NLPDE equation are unearthed. As a result, depending on the dissipative parameter, single and multivalued solutions are depicted. 相似文献
3.
New Periodic Solution to Jacobi Elliptic Functions of a (2+1)-Dimensional BKP Equation and a Generalized Klein-Gordon Equation 下载免费PDF全文
With the help of the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to obtain the Jacobi doubly periodic wave solutions of the (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and the generalized Klein-Gordon equation. The method is also valid for other (1+1)-dimensional and higher dimensional systems. 相似文献
4.
A Bilinear Backlund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation 下载免费PDF全文
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
5.
Xiu-Rong Guo 《理论物理通讯》2016,65(6):735-742
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, in-cluding the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. 相似文献
6.
By using the variable separation approach, which is based on the corresponding Bäcklund
transformation, new exact solutions of a
(1+1)-dimensional nonlinear evolution equation are obtained.
Abundant new soliton motions of the potential field can be
found by selecting appropriate functions. 相似文献
7.
With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding(2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation(BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing(2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the(2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the(2+1)-dimensional AKNS equation(also called the Davey-Stewartson hierarchy), a kind of(2+1)-dimensional Schr¨odinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new(2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the(2+1)-dimensional integrable coupling, which is further reduced to the standard(2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known(1+1)-dimensional AKNS hierarchy, the(1+1)-dimensional nonlinear Schr¨odinger equation are all special cases of the(2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the(2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. 相似文献
8.
9.
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
10.
In this Letter, a new mapping method is proposed for constructing more exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional Konopelchenko-Dubrovsky equation and the (2+1)-dimensional KdV equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained. 相似文献
11.
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
12.
Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations 总被引:1,自引:0,他引:1
With the help of some reductions of the self-dual Yang Mills (briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of (2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new (2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of (2 + 1)-dimensional integrable couplings of a new (2 + 1)- dimensional integrable nonlinear equation. 相似文献
13.
14.
In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived. 相似文献
15.
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1+1)-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method. 相似文献
16.
A nonlinear transformation and some
multi-solition solutions for the (2+1)-dimensional generalized
Broer-Kaup (GBK) system is first given by using the homogeneous
balance method. Then starting from the nonlinear transformation,
we reduce the (2+1)-dimensional GBK system to a simple linear
evolution equation. Solving this equation, we can obtain some new
explicit exact solutions of the original equations
by means of the extended hyperbola function method. 相似文献
17.
ZHANG Huan ;TIAN Bo ;ZHANG Hai-Qiang ;GENG Tao ;MENG Xiang-Hua ;LIU Wen-Jun ;CAI Ke-Jie 《理论物理通讯》2008,50(11):1169-1176
For describing various complex nonlinear phenomena in the realistic world, the higher-dimensional nonlinear evolution equations appear more attractive in many fields of physical and engineering sciences. In this paper, by virtue of the Hirota bilinear method and Riemann theta functions, the periodic wave solutions for the (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev Petviashvili (KP) equation are obtained. Furthermore, it is shown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions. 相似文献
18.
Two Darboux transformations of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka ( CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux trans- formations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water. 相似文献
19.
In this letter, we point out that if there is a (2+1)-dimensional extension of the KdV equation,then we can get a corresponding (2+1)-dimensional sine-Gordon (SG) or sinh-Gordon (SHG) extension which is related to the negative flow equation of the KdV extension. The (2+1)-dimensional SG (or SHG) extensions related to the KP, breaking soliton and Nizhnik-Novikov-Veselov equations are known in literature while the (2+1)-dimensional SHG extension related to the negative Aow equation of the Boiti-Leon-Manna-Pempinelli (BLMP) equation is obtained in this letter thanks to the Schwartz form of the BLMP equation being conformal invariant. 相似文献
20.
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