共查询到20条相似文献,搜索用时 0 毫秒
1.
PENG Yan-Ze 《理论物理通讯》2005,43(2):205-207
New exact solutions in terms of the Jacobi
elliptic functions are obtained to the (2+1)-dimensional breaking
soliton equation by means of the modified mapping method. Limit
cases are studied, and new solitary wave solutions and triangular
periodic wave solutions are obtained. 相似文献
2.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(11)
The singular manifold method is used to obtain two general solutions to a (2 1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
3.
Under investigation is the (2+1)-dimensional breaking soliton equation. Based on a special ansätz functions and the bilinear form, some entirely new double-periodic soliton solutions for the (2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures. 相似文献
4.
Symbolic Computation and Construction of Soliton-Like Solutions to the(2+1)-Dimensional Breaking Soliton Equation 总被引:2,自引:0,他引:2
Based on the computerized symbolic system Maple, a new generalized expansion method of Riccatiequation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new generalansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = 0, uy = vx, and obtain rich new families of the exact solutions of the breaking soliton equation, including thenon-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular functionsolutions. 相似文献
5.
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(5):793-798
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 相似文献
6.
CHENYong LIBiao ZHANGHong-Qing 《理论物理通讯》2003,40(2):137-142
Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions‘ soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2 1)-dimensional breaking soliton equation, ut buxxy 4buvx 4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions. 相似文献
7.
New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 总被引:1,自引:0,他引:1
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(11)
In this paper, the generalized tanh function method is extended to (2 1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2 1)-dimensional CGKP equation with variable coefficients. 相似文献
8.
In this paper, the truncated Painlev′e analysis and the consistent tanh expansion(CTE) method are developed for the(2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is difficult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus m = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. 相似文献
9.
By applying the Lie group method, the (2+1)-dimensional
breaking soliton equation is reduced to some (1+1)-dimensional nonlinear
equations. Based upon some new explicit solutions of the
(2+1)-dimensional breaking soliton equation are obtained. 相似文献
10.
New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients
CHEN Huai-Tang ZHANG Hong-Qing 《理论物理通讯》2004,42(10)
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1 )-dimensional Burgers equation with variable coefficients. 相似文献
11.
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e.,the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures. 相似文献
12.
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
13.
New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients 总被引:1,自引:0,他引:1
CHENHuai-Tang ZHANGHong-Qing 《理论物理通讯》2004,42(4):497-500
A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3 1)-dimensional Burgers equation with variable coefficients. 相似文献
14.
In this paper,by using symbolic and algebra computation,Chen and Wang's multiple Riccati equations rational expansion method was further extended.Many double soliton-like and other novel combined forms of exact solutions of the (2 1 )-dimensional Breaking soliton equation are derived by using the extended multiple Riccati equations expansion method. 相似文献
15.
MA Zheng-Yi LIU Yu-Lu LU Zhi-Ming ZHENG Chun-LongLU Zhi-Ming ZHENG Chun-Long 《理论物理通讯》2006,46(5):799-803
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2+l)-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns. 相似文献
16.
ZHAOQiang LIUShi-Kuo FUZun-Tao 《理论物理通讯》2004,42(2):239-241
The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained. 相似文献
17.
XU Chang-Zhi 《理论物理通讯》2006,46(3):403-406
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately. 相似文献
18.
By means of two different Riccati
equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1)-dimensional dispersive long wave equation are successfully constructed, which include various combination of
trigonometric periodic and hyperbolic function solutions, various
combination of trigonometric periodic and rational function
solutions, and various combination of hyperbolic and rational
function solutions. 相似文献
19.
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2 1)-dimensional dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns. 相似文献
20.
In this letter, we construct a kind of new Darboux transformation for
the (1+1)-dimensional higher-order Broer-Kaup (HBK) system with
the help of a gauge transformation of a spectral problem. By applying
this new Darboux transformation, some new soliton-like solutions of
the (1+1)-dimensional HBK system are obtained. 相似文献