共查询到20条相似文献,搜索用时 15 毫秒
1.
MA Hong-Cai YU Yao-Dong GE Dong-Jie 《理论物理通讯》2009,51(4):609-612
In this paper, the nonlinear dispersive Zakharov- Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found. 相似文献
2.
In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method.These solutions are important for the explanation of some practical physical problems.The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients. 相似文献
3.
New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov Equations Using General Projective Riccati Equation Method 总被引:1,自引:0,他引:1
Applying the generalized method, which is a
direct and unified algebraic method for constructing multiple
travelling wave solutions of nonlinear partial differential
equations (PDEs), and implementing in a computer
algebraic system, we consider the generalized Zakharov-Kuzentsov equation
with nonlinear terms of any order. As a result, we can not only
successfully recover the previously known travelling wave solutions
found by existing various tanh methods and other sophisticated methods,
but also obtain some new formal solutions. The solutions obtained include
kink-shaped solitons, bell-shaped solitons,
singular solitons, and periodic solutions. 相似文献
4.
In this paper, by introducing some appropriate transformation and with the help of symbolic computation, we study exact travelling wave solutions for the high-order modified Boussinesq equation, a single nonlinear reaction-diffusion equation and a generalized nonlinear Schrödinger equation with nonlinear terms of any order by use of the extended-tanh method. Thus, some new exact travelling-wave solutions, which contain kink-shaped solitons, bell-shaped solitons, periodic solutions, combined formal solitons, rational solutions and singular solitons for these equations, are obtained. 相似文献
5.
Some new exact solutions to the Burgers--Fisher equation and generalized Burgers--Fisher equation
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Some new exact solutions of the Burgers--Fisher equation and
generalized Burgers--Fisher equation have been obtained by using the
first integral method. These solutions include exponential function
solutions, singular solitary wave solutions and some more complex
solutions whose figures are given in the article. The result shows
that the first integral method is one of the most effective
approaches to obtain the solutions of the nonlinear partial
differential equations. 相似文献
6.
Zhen-Shu Wen 《理论物理通讯》2018,70(6):672-676
In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center, and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system. 相似文献
7.
Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method.
It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical
field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic
and nonelastic interactions are found. 相似文献
8.
A modified Kadomtsev-Petviashvili(mKP) equation in(3+1) dimensions is presented.We reveal multiple front-waves solutions for this higher-dimensional developed equation,and multiple singular front-wave solutions as well.The constraints on the coefficients of the spatial variables,that assure the existence of these multiple front-wave solutions are investigated.We also show that this equation fails the Pamlevi test,and we conclude that it is not integrable in the sense of possessing the Pain/eve property,although it gives multiple front-wave solutions. 相似文献
9.
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
10.
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
11.
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
12.
The nonlocal nonlinear Schrödinger equation (NNLSE) with competing weakly nonlocal nonlinearity and parabolic law nonlinearity is explored in the current work. A powerful integration tool, which is a modified form of the simple equation method, is used to construct the dark and singular 1-soliton solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical gadget for solving various types of NNLSEs. 相似文献
13.
M S Osman K U Tariq Ahmet Bekir A Elmoasry Nasser S Elazab M Younis Mahmoud Abdel-Aty 《理论物理通讯》2020,72(3):35002-13
The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena. 相似文献
14.
Travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms 总被引:1,自引:0,他引:1
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Applying the general projective Riccati equations method, we consider the exact travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms using symbolic computation.From our results, we not only can successfully recover some previously known travelling wave solutions found by using various tanh methods, but also can obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. 相似文献
15.
PENG Yan-Ze 《理论物理通讯》2010,54(5):863-865
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. Bäcklund transformation in terms ofthe singular manifold is obtained. And localized structures are also investigated. 相似文献
16.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixth-degree nonlinear term, we study the (2 1)-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations. 相似文献
17.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixtb-aegree nonnneal term, we study the (2+l )-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations. 相似文献
18.
New Exact Travelling Wave Solutions to Kundu Equation 总被引:1,自引:0,他引:1
Based on a first-order nonlinear ordinary differential equation with Six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献
19.
Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献
20.
New explicit exact solutions to a nonlinear dispersive-dissipative equation 总被引:1,自引:0,他引:1
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Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive-dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons. 相似文献