共查询到20条相似文献,搜索用时 15 毫秒
1.
GONG Lun-Xun PAN Jun-Ting 《理论物理通讯》2008,50(7):51-52
Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f (ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献
2.
New Solitary Wave Solutions to the KdV-Burgers Equation 总被引:12,自引:0,他引:12
Based on the analysis on the features of the Burgers equation and KdV equation as well as KdV-Burgers equation, a superposition method is proposed to construct the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and KdV equation, and then by using it we obtain many solitary wave solutions to the KdV-Burgers equation, some of which are new ones.PACS: 02.30.Jr; 03.65.Ge 相似文献
3.
New Travelling Wave Solutions to Compound KdV-Burgers Equation 总被引:1,自引:0,他引:1
The compound KdV-Burgers equation and combined KdV-mKdV equation
are real physical models concerning many branches in
physics. In this paper, applying the improved trigonometric function
method to these equations, rich explicit and exact travelling
wave solutions, which contain solitary-wave solutions, periodic
solutions, and combined formal solitary-wave solutions, are
obtained. 相似文献
4.
5.
Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation 总被引:1,自引:0,他引:1
ZHANG Wei-Guo DONG Chun-Yan FAN En-Gui 《理论物理通讯》2006,46(6):1091-1100
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions. 相似文献
6.
ZHANG Wei-Guo DONG Chun-Yan FAN En-Gui 《理论物理通讯》2006,46(12)
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travellingwave form satisfies some special conditions. 相似文献
7.
WANG Ming-Liang ZHANG Jin-Liang LI Xiang-Zheng 《理论物理通讯》2008,50(7):39-42
With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Sehrodinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
8.
ZHENG Qiang REN Zhong-Zhou 《理论物理通讯》2008,49(2):303-304
The double-sine-Gordon equation is studied by means of the so-called mapping method. Some new exact solutions are determined. 相似文献
9.
In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points. 相似文献
10.
A Polynomial Expansion Method and New General Solitary Wave Solutions to KS Equation 总被引:2,自引:0,他引:2
PENG Yan-ze 《理论物理通讯》2003,39(6):641-642
Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation. 相似文献
11.
With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Schrödinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
12.
DU Xing-Hua LIU Cheng-Shi 《理论物理通讯》2006,46(11)
The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new. 相似文献
13.
YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(12)
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
14.
YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(6):1011-1014
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result, many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
15.
A (3+1)-dimensional Gross-Pitaevskii (GP) equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrodinger (NLS) equation. Exact solutions of the (3+1)D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported. 相似文献
16.
In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well
as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers
equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation
are presented successfully by means of this method. 相似文献
17.
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations.
With the aid of symbolic computation, we apply the proposed method
to solving the (1+1)-dimensional dispersive long wave equation and
explicitly construct a series of exact solutions which include the
rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases. 相似文献
18.
A (3+1)-dimensional Gross-Pitaevskii (GP) equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrödinger (NLS) equation. Exact solutions of the (3+1)D GP equation are constructed via those of the NLS equation. By applying specific time-modulated nonlinearities, dispersions, and potentials, the dynamics of the solutions can be controlled. Solitary and periodic wave solutions with snaking and breathing behavior are reported. 相似文献
19.
In this paper, we first consider
exact solutions for Lienard equation
with nonlinear terms of any order.
Then, explicit exact bell and kink profile solitary-wave solutions
for many nonlinear evolution equations are obtained by means of
results of the Lienard equation and proper deductions, which transform
original partial differential equations into the Lienard one.
These nonlinear equations include compound KdV, compound KdV-Burgers,
generalized Boussinesq, generalized KP and Ginzburg-Landau
equation. Some new solitary-wave solutions are found. 相似文献
20.
In this paper, we study the bifurcations and dynamics of traveling wave solutions to a Fujimoto-Watanabe equation by using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the parametric space. Then we show the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, compactions and kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions and periodic wave solutions are implicitly given,while the expressions of kink-like and antikink-like wave solutions are explicitly shown. The dynamics of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of the nonlinear wave. 相似文献