scholarly journals On an Elliptic Function Solution of Kepler's Problem

1877 ◽  
Vol 37 (7) ◽  
pp. 366-386
Author(s):  
J. W. L. Glaisher
Keyword(s):  
Elliptic Function ◽  
Function Solution ◽  
Kepler’S Problem

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.

Optical solitons in parabolic law medium: Jacobi elliptic function solution

2016 ◽  
Vol 85 (4) ◽  
pp. 2577-2582 ◽  
Author(s):  
Fairouz Tchier ◽  
Ebru Cavlak Aslan ◽  
Mustafa Inc
Keyword(s):  
Elliptic Function ◽  
Optical Solitons ◽  
Jacobi Elliptic Function ◽  
Function Solution ◽  
Parabolic Law

JACOBI ELLIPTIC FUNCTION SOLUTION OF GINZBURG–LAUDAU EQUATION BASED ON BCS THEORY

2011 ◽  
Vol 25 (28) ◽  
pp. 2203-2208
Author(s):  
CHUNHUAN XIANG
Keyword(s):  
Elliptic Function ◽  
Landau Equation ◽  
Expansion Method ◽  
Phase Factor ◽  
Bcs Theory ◽  
Jacobi Elliptic Function ◽  
Ginzburg Landau ◽  
Function Solution ◽  
Ginzburg Landau Equation

The GL (Ginzburg–Landau) equation is a very important equation in superconductivity, which can be employed to explain many phenomena. In the present work, by using the expanded F-expansion method, some new exact Jacobi elliptic function solutions of the equation are obtained. More important is the phase factor of the solutions.

scholarly journals The Vibrations of a Particle about a Position of Equilibrium—Part 2 :The Relation between the Elliptic Function and Series Solutions

1921 ◽  
Vol 40 ◽  
pp. 34-49 ◽  
Author(s):  
Bevan B. Baker
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Elliptic Function ◽  
Degrees Of Freedom ◽  
Elliptic Functions ◽  
Series Solutions ◽  
Two Degrees Of Freedom ◽  
Function Solution

In a previous paper, entitled the “Vibrations of a Particle about a Position of Equilibrium,” by the author in collaboration with Professor E. B. Ross (Proc. Edin. Math. Soc., XXXIX, 1921, pp. 34–57), a particular dynamical system having two degrees of freedom was chosen and solutions of the corresponding differential equations were obtained in terms of periodic series and also in terms of elliptic functions. It was shown that for certain values of the frequencies of the principal vibrations, the periodic series become divergent, whereas the elliptic function solution continues to give finite results.

scholarly journals Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Zeid I. A. Al-Muhiameed ◽  
Emad A.-B. Abdel-Salam
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Jacobi Elliptic Function ◽  
Nonlinear Schrödinger ◽  
Function Solution ◽  
Balance Principle ◽  
Wave Solutions

With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.

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