共查询到19条相似文献,搜索用时 93 毫秒
1.
2.
3.
4.
扩展了最近提出的F展开方法以构造非线性演化方程更多的精确解,即将F展开法中的一阶非线性常微分方程和单变量的有限幂级数代之以类似的一阶常微分方程组和两个变量的有限幂级数,这两个变量是一阶常微分方程组的解分量.作为例子,用扩展的F展开法解非线性Schroedinger方程,得到了很丰富的包络形式的精确解,特别是以两个不同的Jacobi椭圆函数表示的解.显然,扩展的F展开方法也可以解其他类型的非线性演化方程. 相似文献
5.
6.
7.
建立了插值矩阵法的基本理论,用于解非线性混合阶常微分方程组多点边值问题,制作了常微分方程组求解器IVMMS,可以支持计算力学中的有限元线法。 相似文献
8.
9.
10.
用函数和方程变换将二阶耦合线性微分方程组转化为一阶非线性类椭圆方程,并给出了一次和二次限定变换下方程组的Jacobi椭圆函数解析解,所得结果修正了文献中超导特例的近似解,进一步肯定了超导边界层电场的存在性.
关键词:
微分方程
Jacobi椭圆函数
解析解
超导 相似文献
11.
A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations 下载免费PDF全文
In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations. 相似文献
12.
为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方 程和Riccati方程的求解问题. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解.
关键词:
常微分方程
非线性叠加公式
高维非线性发展方程
无穷序列类孤子新解 相似文献
13.
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
14.
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
15.
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
16.
LI Hua-Mei 《理论物理通讯》2003,39(4)
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained. 相似文献
17.
用把方程的解设为余弦函数多项式的一种直接方法,求解了受幂律引力作用的质点一类非线性轨道微分方程,从而得出在幂律引力作用下从拱点抛出质点的运动轨道是正弦螺线。 相似文献
18.
In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance
method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified
way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative
equations are investigated by this method and multiple soliton solutions are found. 相似文献
19.
The constructive technique and its application in solving a nonlinear reaction diffusion equation 下载免费PDF全文
A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances. 相似文献