scholarly journals Dynamical properties of the derivative of the Weierstrass elliptic function

2009 ◽  
Vol 2 (3) ◽  
pp. 267-288
Author(s):  
Jeff Goldsmith ◽  
Lorelei Koss
Keyword(s):  
Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Dynamical Properties

scholarly journals Simultaneous approximation of et and ℘(t)

1982 ◽  
Vol 33 (2) ◽  
pp. 171-178
Author(s):  
K. Saradha
Keyword(s):  
Complex Number ◽  
Elliptic Function ◽  
Simultaneous Approximation ◽  
Algebraic Numbers ◽  
Weierstrass Elliptic Function ◽  
Algebraic Invariants ◽  
Image Position

AbstractLet t be any complex number different from the poles of a Weierstrass elliptic function ℘(z), having algebraic invariants. Then we estimate from below the sum where α and β are algebraic numbers. The estimate is given in terms of the heights of α and β and the degree of the field Q(α, β), where Q is the field of rationals.

Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS

2011 ◽  
Vol 25 (14) ◽  
pp. 1931-1939 ◽  
Author(s):  
LIANG-MA SHI ◽  
LING-FENG ZHANG ◽  
HAO MENG ◽  
HONG-WEI ZHAO ◽  
SHI-PING ZHOU
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Order Derivative ◽  
First Order ◽  
Function Solution ◽  
Weierstrass Elliptic Function ◽  
Klein Gordon

A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.

scholarly journals New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Peng Guo ◽  
Xiang Wu ◽  
Liangbi Wang
Keyword(s):  
Elliptic Function ◽  
Finite Deformation ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Elastic Rod ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.

scholarly journals Weierstrass elliptic difference equations

1987 ◽  
Vol 35 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Renfrey B. Potts
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Elliptic Function ◽  
Order Differential Equation ◽  
Second Order ◽  
Elliptic Difference ◽  
First Order ◽  
Second Order Differential Equation ◽  
Weierstrass Elliptic Function

The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.

scholarly journals Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelfattah El Achab
Keyword(s):  
Wave Equation ◽  
Elliptic Function ◽  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Generalized Boussinesq Equation

Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

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