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Volume 23: Pages 276-284, 2010

Exact soliton solutions of the discrete modified Korteweg–de Vries (mKdV) equation

Yufeng Zhang 1,2,3, Jianqin Mei 1,2,3, Y. C. Hon 1,2,3

1College of Science, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China

2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People’s Republic of China

3Department of Mathematics, City University of Hong Kong, People’s Republic of China

By employing elliptic functions and hyperbolic functions, some exact periodic wave solutions, kink-type soliton solutions, and other types of exact traveling-wave solutions to the discrete modified Korteweg–de Vries equation are obtained by using homogenous balance principle. The way presented in the paper can be used to other differential-difference equations extensively.

Keywords: Soliton Solution, Discrete mKdV Equation, Elliptic Function

Received: August 7, 2009; Accepted: March 4, 2010; Published Online: April 6, 2010