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1.
2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting to the Hirota bilinear method. In this paper, N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation are obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs. 相似文献
2.
New Periodic Solution to Jacobi Elliptic Functions of a (2d-1)-Dimensional BKP Equation and a Generalized Klein-Gordon Equation
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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
3.
In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a (1+1)- dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili (KP) equation are obtained. 相似文献
4.
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
5.
In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+ 1)-dimensional KK equation by the symmetry method and the (G1/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. 相似文献
6.
Recently,a new decomposition of the (2 1)-dimensional Kadomtsev-Petviashvili(KP) equation to a (1 1)-dimensional Broer-Kaup (BK) equation and a (1 1)-dimensional high-order BK equation was presented by Lou and Hu.In our paper,a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems.As application,new explicit soliton-like solutions with five arbitrary parameters for the BK equation,high-order BK equation and KP equation are obtained. 相似文献
7.
HU Xiao-Rui CHEN Yong 《理论物理通讯》2008,50(11):1055-1060
On bases of the direct method developed by Clarkson and Kruskal [J. Math. Phys. 27 (1989) 2201], the (2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1 +1)- dimensional partial differential equations. We focus on solving the third type of reduction and dividing them into three subcases, from which we obtain rich solutions including some arbitrary functions. 相似文献
8.
Algebro-Geometric Solution to Two New (2+1)-Dimensional Modified Kadomtsev-Petviashvili Equations
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Two new (2+1)-dimensional modified Kadomtsev-Petviashvili (mKP) equations are presented, which are related to a hierarchy of (1+1)-dimensional soliton equations. Through the nonlinearization of Lax pair and the Riemann-Jacobi inversion technique, the algebro-geometric solutions of both the mKP equations are obtained. 相似文献
9.
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
10.
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (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
11.
2N line-soliton solutions of the
(3+1)-dimensional Jimbo-Miwa equation can be presented by resorting
to the Hirota bilinear method. In this paper, N periodic-soliton
solutions of the (3+1)-dimensional Jimbo-Miwa equation are obtained
from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs. 相似文献
12.
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
13.
Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation 总被引:2,自引:0,他引:2
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Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtadned. 相似文献
14.
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic
potential vorticity equation
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By means of the reductive perturbation method, three types
of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP)
equations are derived from the baroclinic potential vorticity (BPV)
equation, including the modified KP (mKP) equation, standard KP equation
and cylindrical KP (cKP) equation. Then some solutions of
generalized cKP and KP equations with certain conditions are given
directly and a relationship between the generalized mKP equation and
the mKP equation is established by the symmetry group direct method
proposed by Lou et al. From the relationship and the solutions
of the mKP equation, some solutions of the generalized mKP equation can be
obtained. Furthermore, some approximate solutions of the baroclinic
potential vorticity equation are derived from three types of
generalized KP equations. 相似文献
15.
16.
We extend the (1+1)-dimensioanl Sharma-Tasso-Olver (STO) equation to a (2+1)-dimensional one by adding one additional term uyy. A tri-linear form of the (2+1)-dimensional STO equation is obtained by the Painlevé analysis. A family of rational solutions for the (2+1)-dimensional STO equation is constructed by using the resulting tri-linear form. Associated 3-dimensional plot and density plot with particular choices of the involved parameters are given to show the charateristics of the rational solutions. 相似文献
17.
In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G, /G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. 相似文献
18.
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
19.
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
20.
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