elliptic modular function

By using the elliptic function and conformal transformation theory,a close form solution to this problem is obtained.

运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。

Phase plane properties of an electron in Wiggler field are analysed by using Jacobian elliptic function and elliptic integral based on the pendulum equation for FEL.

从自由电子激光器的摆方程出发,利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征,并利用加速器概念和束流动力学方法,讨论了系统的稳定性、增益和临界特征等问题。

A class of new doubly periodic wave solutions for(2+1)-dimensional breaking soliton equation are obtained by introducing appropriate Jacobi elliptic function and Weierstrass elliptic function in the general solution(contains two arbitrary functions)got by means of multilinear variable separation approach for(2+1)-dimensional breaking soliton equation.

在多线性分离变量法所得(2+1)维破裂孤子方程广义解(包含2个任意函数)中引入符合条件的Jacobi椭圆函数和Weierstrass椭圆函数,从而获得了该系统的新双周期解。

Some new exact solutions of the Jacobi elliptic functions of NLS equation;

非线性薛定谔方程的Jacobi椭圆函数解

Using Jacobi elliptic functions expansion method and a modified Hyperbolic-Tan function method,homogenous balancing method,construct the exact solution of nonlinear evolution equations;then using Mathematica software,the solitary wave solutions of the kind of nonlinear evoluation equations are obtained successfully.

利用Jacobi椭圆函数展开法和双曲正切法,结合齐次平衡法构造非线性偏微分方程的精确解,并利用计算机代数系统Mathematica,求得一类非线性发展方程的孤立波解。

By using Mathematica and the F-expansion method recently proposed on the base of analogic method,homogeneous balance method and Jacobi method,the double periodic wave solutions expressed by Jacobi elliptic functions for the(n+1)-dimensional Sinh-Gordon equation .

然后由行波约化将其常微分方程化,在拟设法、齐次平衡法和Jacobi椭圆函数法的基础上,借助Mathematica软件和新近提出的F-展开法,求出并研究了(n+1)维SG方程的Jacobi椭圆函数表示的双周期波解,分析了解的结构,在极限情况下这些解退化为相应的孤立波解、三角函数解和奇异行波解。

The earliest automorphic functions to be studied were the elliptic modular functions.

研究得最早的自导函数是椭圆模函数。

Weierstrass elliptic function solutions for MKdV equations;

MKdV方程的Weierstrass椭圆函数解

Simulating Rice Leaf Angle Inclination Distribution by Elliptical Distribution Function

椭圆分布函数模拟水稻冠层叶倾角分布

A Relationship Between the Hasse-Weil Zeta Function of an Elliptic Curve and Those of its Forms

椭圆函数和它的form的Hasse-Weil Zeta函数的一个关系

The Analysis of the Best Window Function Based on PSWF

基于椭圆球面波函数的最佳窗函数分析

Liouville Theorem and Green Function for Degenerate Elliptic Equations;

退化椭圆型方程的Liouville定理及Green函数

The Equivalence of Discrete Logarithms between Elliptic Curve and Real Quadratic Function Field;

椭圆曲线与实二次函数域的DLP等价

Elliptic Genera and Theta Functions Identities;

椭圆亏格及theta函数的恒等式

Exact Analysis of Single Pendulum by Jacobi Ellipse Function;

利用Jacobi椭圆函数精确分析单摆的运动

Historical Analysis on the Theory of the Elliptic Function;

雅可比建立椭圆函数理论的历史分析

Jacobi Elliptic Function Expansion Method To KdV Equations;

KdV方程的Jacobi椭圆函数求解

New Jacobian elliptic function solutions for nonlinear evolution equations

非线性演化方程的新Jacobi椭圆函数解

Energy Concentration Analysis of Bandpass Prolate Spheroidal Wave Functions

带通椭圆球面波函数能量聚集性分析

A Solution of a Revolving Single Pendulum usIng Jacobi Elliptic Function

“旋转单摆”的Jacobi椭圆函数解

The Jacobi Elliptic Function Solutions for Several Nonlinear Partial Differential Equations;

几种非线性偏微分方程的Jacobi椭圆函数解

The Applications of Jacobi Elliptic Function in Solving Nonlinear Evolution Equations;

Jacobi椭圆函数在求解非线性发展方程中的应用

Weierstrass Elliptic Function Solutions to a New Type of NLS Equations;

一类非线性薛定谔方程的Weierstrass椭圆函数解

Jacobi Elliptic Function Expansion Methed to a New Type of NLS Equations;

一类非线性薛定谔方程的Jacobi椭圆函数解