On Weierstrass elliptic function solutions for a (N+1) dimensional potential KdV equation

2011 ◽  
Vol 217 (20) ◽  
pp. 8080-8092 ◽  
Author(s):  
Yunxi Guo ◽  
Ying Wang
Keyword(s):  
Elliptic Function ◽  
Kdv Equation ◽  
Weierstrass Elliptic Function

scholarly journals F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ali Filiz ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
New Exact Solutions

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulusmof Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

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.

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