共查询到20条相似文献,搜索用时 15 毫秒
1.
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the
x-axis. In this paper, with the aid of symbolic computation, six
kinds of new special exact soltion-like solutions of
(2+1)-dimensional breaking soliton equation are obtained by using
some general transformations and the further generalized
projective Riccati equation method. 相似文献
2.
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
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.
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
5.
The consistent tanh expansion (CTE) method is employed to the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters. 相似文献
6.
Using the standard truncated Painlevé analysis, we have obtained some special types of exact explicit solitary wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvilli equations. Usually, one obtains the single solitary wave solution from the Backlund transformation related to the truncated Painlevé analysis starting from the trivial vacuum solution. In this letter, we find some special types of the multi-solitary wave solution from the truncated Painlevé analysis and the trivial vacuum solution. 相似文献
7.
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic. 相似文献
8.
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
9.
Based on the Pfaffian derivative formulae, a Grammian determinant solution for a (3+1)-dimensional soliton equation is obtained. Moreover, the Pfaffianization procedure is applied for the equation to generate a new coupled system. At last, a Gram-type Pfaffian solution to the new coupled system is given. 相似文献
10.
A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献
11.
PENG Yan-Ze 《理论物理通讯》2004,41(5):669-670
A new multisoliton solution to the
(2+1)-dimensional KdV equation is obtained by means of the
truncated Painleve expansion method and a direct ansatz technique.
This new exact solution is periodic in the propagating direction
x and exponentially decaying in y and thus it is called
periodic solitons. A typical spatial structure of it is
illustrated by the figures. 相似文献
12.
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
13.
ZHAO Hong BAI Cheng-Lin 《理论物理通讯》2004,42(10)
Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed. 相似文献
14.
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
15.
The variable separation approach is used to obtain localized coherent structures of the new (2 1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks. 相似文献
16.
In a recent paper [Commun. Theor. Phys. (Beijing, China) 49 (2008) 268], Huang et al. gave a general variable separation solution to the (2+1)-dimensional breaking soliton equation via a special Biicldund transformation and the variable separation approach. In terms of the derived variable separation solution and by introducing Jacobi elliptic functions, they claimed that nonelastic types of interaction between Jacobi elliptic function waves are investigated both analytically and graphically. We show that some inappropriateness or errors exist in their paper, and say nothing of the conclusion that some nonelastic types of interaction between Jacobi elliptic function waves in the (2+1)-dimensional breaking soliton equation have been found. 相似文献
17.
The algebraic mapping relations between the (2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein—Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves, Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions. 相似文献
18.
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
19.
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
20.
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