共查询到20条相似文献,搜索用时 0 毫秒
1.
Based on a transformed Painlevé property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painlevé property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. 相似文献
2.
ZHANG Lin-Na FU Zun-Tao LIU Shi-Kuo 《理论物理通讯》2008,50(7):48-50
In this paper, dependent and independent variable transformations are introduced to solve the Degasperis- Procesi equation. It is shown that different kinds of solutions can be obtained to the Degasperis-Procesi equation. 相似文献
3.
In this paper, dependent and independent variable transformations
are introduced to solve the Degasperis-Procesi equation. It is shown
that different kinds of solutions can be obtained to the
Degasperis-Procesi equation. 相似文献
4.
New Exact Solutions to the Combined KdV and mKdV Equation 总被引:2,自引:0,他引:2
Yan-ze Peng 《International Journal of Theoretical Physics》2003,42(4):863-868
The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration. 相似文献
5.
FU Zun-Tao ZHENG Ming-Hua LIU Shi-Kuo 《理论物理通讯》2009,51(3):395-396
In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation. 相似文献
6.
In this paper, two transformations are introduced to solve
sinh-Gordon equation by using the knowledge of elliptic equation
and Jacobian elliptic functions. It is shown that different
transformations are required in order to obtain more kinds of
solutions to the sinh-Gordon equation. 相似文献
7.
In this paper, four transformations are introduced to solve single sine-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the single sine-Gordon equation. 相似文献
8.
FUZun-Tao YAOZhen-Hua LIUShi-Kuo LIUShi-Da 《理论物理通讯》2005,44(1):23-30
In this paper, four transformations are introduced to solve single sine-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the single sine-Gordon equation. 相似文献
9.
In this paper, a new transformation is introduced to solve triple
sine-Gordon equation. It is shown that this intermediate
transformation method is powerful to solve complex special type
nonlinear evolution equation. 相似文献
10.
DENG Shu-Fang 《理论物理通讯》2005,43(6):961-964
The bilinear form for a nonisospectral and variable-coefficient KdV equation
is obtained and some exact soliton solutions are derived through
Hirota method and Wronskian technique. We also derive the bilinear
transformation from its Lax pairs and find solutions with
the help of the obtained bilinear transformation. 相似文献
11.
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
12.
HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(2):171-174
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
13.
Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case,
the solitary wave solution to NNV equation are also obtained. 相似文献
14.
The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients. 相似文献
15.
smail Aslan 《理论物理通讯》2014,(5):595-599
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. 相似文献
16.
17.
Reza Mokhtari 《理论物理通讯》2011,55(2):204-208
The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. 相似文献
18.
In this paper, new Jacobi elliptic function solutions of
multi-component mKdV equation are obtained directly in a unified
way. When the modulus m→1, those periodic solutions
degenerate as the corresponding hyperbolic function solutions.
Then, to the three-component mKdV equation, five types of
effective solution are presented in detail. 相似文献
19.
Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method
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By introducing a more general auxiliary ordinary differential equation (ODE), a modified
variable separated ODE method is
developed for solving the mKdV--sinh-Gordon equation. As a result,
many explicit and exact solutions including some new formal
solutions are successfully picked up for the mKdV--sinh-Gordon
equation by this approach. 相似文献
20.
The two-dimensional (2D) nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic
potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the
Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodic-wave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 2D Rossby soliton solutions are also obtained. 相似文献