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1.
Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations. 相似文献
2.
ZHANG Jie-Fang HUANG Wen-Hua 《理论物理通讯》2001,(11)
Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2 1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2 1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations.`` 相似文献
3.
In the present letter, we get the appropriate bilinear forms of(2+1)-dimensional KdV equation, extended (2+1)-dimensional shallow water wave equation and (2+1)-dimensional Sawada-Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions. 相似文献
4.
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
5.
The (2+l)-dimensional Korteweg-de Vries (KdV) equation proposed recently by Levi is extended to a higher order (2+1)-dimensional KdV equation from water wave dynamics when considering surface tension. Its exact and explicit solitary wave solutions can be obtained by relating it to the higher order KdV equation. 相似文献
6.
According to the conjecture based on some known facts of integrable
models, a new (2+1)-dimensional supersymmetric integrable bilinear
system is proposed. The model is not only the extension of the known
(2+1)-dimensional negative Kadomtsev--Petviashvili equation but also
the extension of the known (1+1)-dimensional supersymmetric
Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro
symmetries and the related symmetry reductions of the model are
obtained. Furthermore, the traveling wave solutions including
soliton solutions are explicitly presented. 相似文献
7.
ZHANG JieFang 《理论物理通讯》1999,32(2):315-318
By using a homogeneous balance method, we give new soliton-like solutions for the (2+1)-dimensional KdV equation and the (2+1)-dimensional breaking soliton equation. Solitary wave soIutions are shown to be a special case of the present results. 相似文献
8.
Higher-Dimensional Integrable Systems Induced by Motions of Curves in Affine Geometries 总被引:1,自引:0,他引:1
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We discuss the motions of curves by introducing an extra spatial variable or equivalently, moving surfaces in arffine geometries. It is shown that the 2 +1-dimensional breaking soliton equation and a 2 + 1-dimensional nonlinear evolution equation regarded as a generalization to the 1 + 1-dimensional KdV equation arise from such motions. 相似文献
9.
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
10.
Using some limiting procedures, the solutions of the fifth order KdV equation ut + (μu2+ υuxx + αuuxx + βux2 + γu3 + δuxxxx)x = 0 would degenerate into the solutions of a simple equation, say KdV equation. In this letter, we analyze the possibility of the inverse procedure of the limiting process mentioned above for the travelling wave solutions. The results show that the procedure for deforming a travelling wave solution of the KdV equation to that of the generalized fifth order KdV equation can be accomplished by some pure algebraic tricks. Moreover, this inverse procedure is not unique in general. 相似文献
11.
In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained. 相似文献
12.
In this paper, using the generalized G'/G-expansion method and the auxiliary differential equation method, we discuss the (2+1)-dimensional canonical generalized KP (CGKP), KdV, and (2+1)-dimensional Burgers equations with variable coefficients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions. 相似文献
13.
CAO Ce-Wen YANG Xiao 《理论物理通讯》2008,49(1):31-36
Special solution of the (2+1)-dimensional Sawada Kotera equation is decomposed into three (0+1)- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy. 相似文献
14.
The multi-linear variable separation approach method is very useful to solve
(2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers
system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from
many (2+1)-dimensional systems is extended or modified. 相似文献
15.
The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations. 相似文献
16.
LOU Senyue 《理论物理通讯》1997,28(2):129-132
A (3+1)-dimensional model is proposed at first. The integrability of the model is proved by using the standard Painlevk analysis. Then the model is extended to (n + 1)-dimensional case. The model is space-isotropic and is a type of the modified KdV extension in higher dimensions. 相似文献
17.
A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated. 相似文献
18.
19.
New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer- Kaup- Kupershmidt system
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Some new exact solutions of an auxiliary ordinary differential
equation are obtained, which were neglected by Sirendaoreji {\it et
al in their auxiliary equation method. By using this method and
these new solutions the combined Korteweg--de Vries (KdV) and
modified KdV (mKdV) equation and (2+1)-dimensional
Broer--Kaup--Kupershmidt system are investigated and abundant exact
travelling wave solutions are obtained that include new solitary wave
solutions and triangular periodic wave solutions. 相似文献
20.
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