共查询到20条相似文献,搜索用时 15 毫秒
1.
HU Heng-Chun LOU Sen-Yue 《理论物理通讯》2004,42(10)
The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor-Carnvale Painleve truncation expansion and the nonstandard truncation of a modified Conte‘s invariant Painleve expansion. 相似文献
2.
The special soliton solutions of Bogoyavlenskii coupled KdV equations
are obtained by means of the standard Weiss-Tabor-Carnvale Painlev\'{e}
truncation expansion and the nonstandard truncation of a modified Conte's
invariant Painlev\'{e} expansion. 相似文献
3.
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained. 相似文献
4.
Based on the invariant expansion method,some reasonable approximate solutions of coupled Korteweg-de Vries(KdV)equations with diferent linear dispersion relations have been obtained.These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacobi elliptic functions.The results also show that if the arbitrary constants are selected suitably,the approximate solutions may become the exact ones. 相似文献
5.
Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries (KdV) equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones. 相似文献
6.
7.
QIAN Su-Ping TIAN Li-Xin 《理论物理通讯》2007,48(3):399-404
Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations. 相似文献
8.
Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations. 相似文献
9.
Lie Point Symmetries and Exact Solutions of Couple KdV Equations 总被引:4,自引:0,他引:4
QIAN Su-Ping TIAN Li-Xin 《理论物理通讯》2007,47(4):582-586
The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc. 相似文献
10.
11.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,50(10):809-813
A special coupled KdV equation is proved to be the Painleve property by the Kruskal's simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota's bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically. 相似文献
12.
For a special coupled Korteweg de Vries (KdV) system, its similarity solutions and reduction equations are obtained by the Clarkson and Kruskal's direct method. In addition, its new explicit soliton solutions and traveling wave solutions are found by the deformation and mapping method. 相似文献
13.
In this paper, by introducing a new transformation, the bilinear
form of the coupled integrable dispersionless (CID) equations is
derived. It will be shown that this bilinear form is easier to
perform the standard Hirota process. One-, two-, and three-soliton
solutions are presented. Furthermore, the N-soliton solutions are
derived. 相似文献
14.
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
15.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,49(1):22-26
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift. 相似文献
16.
HUANG Ye-Hui WU Hong-Xia XIE Xi ZENG Yun-Bo 《理论物理通讯》2008,49(5):1091-1100
The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS. 相似文献
17.
The Hirota-Satsuma coupled KdV equations associated 2×2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator. 相似文献
18.
YONG Xue-Lin CHEN Yu-Fu 《理论物理通讯》2008,50(7):43-47
In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless (CID) equations is derived. It will be shown that this bilineax form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Furthermore, the N-soliton solutions axe derived. 相似文献
19.
Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV(GCCKdV) equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonic collisions are presented: (i) two solitons merge and separate fromeach other periodically; (ii) two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; (iii) two solitons are fluctuant in the central region of the collision. Propagation features ofsolitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the α increasing. Amplitude of v increase with the α increasing and decrease with the β increasing. 相似文献
20.
The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions. 相似文献