共查询到18条相似文献,搜索用时 62 毫秒
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利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性 Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组). 相似文献
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立方非线性Schr(o)dinger方程的Weierstrass椭圆函数周期解 总被引:1,自引:1,他引:1
利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组). 相似文献
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利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性Schrdinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组). 相似文献
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李德生 《原子与分子物理学报》2006,23(5):933-937
将文[22]中提出的求解非线性演化方程的Weierstrass椭圆函数解的一个新方法应用于Time Dependent Ginzburg-Landau方程,获得了该方程的一些新的双周期解,并在退化情形下得到了一些新的精确孤波解. 相似文献
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This paper is based on the relations between projection
Riccati equations and Weierstrass elliptic equation, combined with the
Groebner bases in the symbolic computation. Then the novel method for
constructing the Weierstrass elliptic solutions to the nonlinear evolution
equations is given by using the above relations. 相似文献
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YAN Zhen-Ya 《理论物理通讯》2005,43(3):391-396
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem
solving soliton equations into
another one solving the corresponding set of nonlinear algebraic equations.
With the aid of Maple, we choose the modified KdV equation,
(2+1)-dimensional KP equation,
and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm.
As a consequence, many types of new doubly periodic solutions are obtained
in terms of the Weierstrass elliptic function. Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple
limits of doubly periodic solutions. 相似文献
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A. H. Khater M. M. Hassan E. V. Krishnan Y. Z. Peng 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(2):177-184
New several classes of exact solutions are obtained in terms of the
Weierstrass elliptic function for some nonlinear partial
differential equations modeling ion-acoustic waves as well as dusty
plasmas in laboratory and space sciences. The Weierstrass elliptic
function solutions of the Schamel equation, a fifth order dispersive
wave equation and the Kawahara equation are constructed. Moreover,
Jacobi elliptic function solutions and solitary wave solutions of
the Schamel equation are also given. The stability of some periodic
wave solutions is computationally
studied. 相似文献
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YANZhen-Ya 《理论物理通讯》2004,42(5):645-648
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献
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An improved algorithm is devised for using Fan sub-equation method to solve Wick-type stochastic partial differential equations. Applying the improved algorithm to the Wick-type generalized stochastic KdV equation, we obtain more general Jacobi and Weierstrass elliptic function solutions, hyperbolic and trigonometric function solutions, exponential function solutions and rational solutions. 相似文献
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By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解.
关键词:
第二种椭圆方程
Riccati方程
非线性发展方程
Riemann theta 函数无穷序列解 相似文献
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New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm 总被引:1,自引:0,他引:1
YAN Zhen-Ya 《理论物理通讯》2004,42(11)
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献