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1.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
2.
YAN Zhen-Ya 《理论物理通讯》2002,38(4):400-402
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again
by using a new transformation, which and our extended Jacobian elliptic
function expansion method form a new method still called the
extended Jacobian elliptic function expansion method. The new method can
be more powerful to be applied to other nonlinear differential equations. 相似文献
3.
YAN Zhen-Ya 《理论物理通讯》2003,39(2)
More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations. 相似文献
4.
提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解
关键词:
试探方程法
非线性发展方程
孤波解
Jacobi椭圆函数
周期解 相似文献
5.
Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation
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By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 相似文献
6.
GE Jian-Ya WANG Rui-Min DAI Chao-Qing ZHANG Jie-Fang 《理论物理通讯》2006,46(4):656-662
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
7.
8.
The Jacobian elliptic function expansion method for nonlinear
differential-different equations and its algorithm are presented
by using some relations among ten Jacobian elliptic functions and
successfully construct more new exact doubly-periodic solutions of
the integrable discrete nonlinear Schr ödinger equation. When the
modulous m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark
soliton, new solitons as well as trigonometric function solutions. 相似文献
9.
YAN Zhen-Ya 《理论物理通讯》2002,38(2):143-146
An extended Jacobian elliptic function
expansion method presented recently by us is applied to the mKdV equation such
that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus
m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to
other nonlinear differential
equations. 相似文献
10.
In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution. 相似文献
11.
12.
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
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In this paper, the improved Jacobian elliptic function expansion
approach is extended and applied to constructing discrete solutions
of the semi-discrete coupled modified Korteweg de Vries (mKdV)
equations with the aid of the symbolic computation system Maple.
Some new discrete Jacobian doubly periodic solutions are obtained.
When the modulus $m \rightarrow 1$, these doubly periodic solutions
degenerate into the corresponding solitary wave solutions, including
kink-type, bell-type and other types of excitations. 相似文献
13.
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
14.
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
15.
16.
A new approach is presented by means of a new general ansätz and some relations among Jacobian elliptic
functions, which enables one to construct more new exact solutions
of nonlinear differential-difference equations. As an example, we
apply this new method to Hybrid lattice, discretized mKdV lattice,
and modified Volterra lattice. As a result, many exact solutions
expressible in rational formal hyperbolic and elliptic functions
are conveniently obtained with the help of Maple. 相似文献
17.
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
18.
General Jacobian elliptic function expansion method and its applications 总被引:11,自引:0,他引:11
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An extended Jacobian elliptic function expansion method is presented and successfully applied to the nonlinear Schr?dinger (NLS) equation and Zakharov equation. We obtain some new solutions besides Fu et al's results. The results show that our method is more powerful to construct Jacobian elliptic function and can be applied to other nonlinear physics systems. 相似文献
19.
In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution. 相似文献
20.
ZHANG Ling ZHANG Li-Feng LI Chong-Yin WANG Tie TAN Yan-Ke 《理论物理通讯》2008,49(6):1557-1560
By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 相似文献