New exact solutions of the (n+1)-dimensional sine-Gordon equation using double elliptic equation method

Abstract

In this paper, the (n+1)-dimensional sine-Gordon equation is studied using double elliptic equation method. With the aid of Maple, more exact solutions expressed by Jacobi elliptic functions are obtained. When the modulus m of Jacobi elliptic function is driven to the limit 1 and 0, some exact solutions expressed by hyperbolic function solutions and trigonometric functions can also be obtained, respectively.

Keywords:

• (n+1)-dimensional sine-Gordon equation
• double elliptic equation method
• exact solution
• Jacobi elliptic function

PACS :

• 02.30.Ik
• 02.30.Jr
• 02.70.−c
• 05.10.−a
• 05.45.Yv

Acknowledgements

This research was supported by Natural Science Foundation of Yunnan Province, China (2007A080M) and the National Natural Science Foundation of China (10571062). We thank the referees^, valuable suggestions.