Painleve’ analysis of a variable coefficient Sine‐Gordon equation

1995 ◽  
Vol 5 (4) ◽  
pp. 690-692 ◽  
Author(s):  
Angelo Di Garbo ◽  
Leone Fronzoni
Keyword(s):  
Variable Coefficient ◽  
Gordon Equation ◽  
Painlevé Analysis ◽  
Sine Gordon Equation ◽  
Painleve Analysis

scholarly journals Painlevé Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Xiaoxiao Zheng ◽  
Fanning Meng
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Kdv Equation ◽  
Painlevé Analysis ◽  
Complex Method ◽  
Meromorphic Solutions ◽  
Sine Gordon Equation ◽  
Algebraic Differential Equations ◽  
Painleve Analysis

In this paper, a class of nonlinear algebraic differential equations (NADEs) is studied. The Painlevé analysis of the NADEs is considered. Abundant meromorphic solutions of the NADEs are obtained by means of the complex method. Then, meromorphic exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and (2+1)-dimensional sine-Gordon equation are derived via the applications of the NADEs.

scholarly journals Analytical solutions of differential-difference sine-Gordon equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1701-1705 ◽  
Author(s):  
Da-Jiang Ding ◽  
Di-Qing Jin ◽  
Chao-Qing Dai
Keyword(s):  
Elliptic Function ◽  
Variable Coefficient ◽  
Gordon Equation ◽  
Variable Coefficients ◽  
Jacobian Elliptic Function ◽  
Sine Gordon Equation ◽  
Electron Conduction ◽  
Negative Power ◽  
Non Linear ◽  
Linear Differential

In modern textile engineering, non-linear differential-difference equations are often used to describe some phenomena arising in heat/electron conduction and flow in carbon nanotubes. In this paper, we extend the variable coefficient Jacobian elliptic function method to solve non-linear differential-difference sine-Gordon equation by introducing a negative power and some variable coefficients in the ansatz, and derive two series of Jacobian elliptic function solutions. When the modulus of Jacobian elliptic function approaches to 1, some solutions can degenerate into some known solutions in the literature.

Painlevé analysis and some solutions of variable coefficient Benny equation

Pramana ◽  
2015 ◽  
Vol 85 (6) ◽  
pp. 1111-1122 ◽  
Author(s):  
RAJEEV KUMAR ◽  
R K GUPTA ◽  
S S BHATIA
Keyword(s):  
Variable Coefficient ◽  
Painlevé Analysis ◽  
Painleve Analysis
Sign in / Sign up

Export Citation Format

Share Document