Soliton Solutions of Discrete Complex Ginzburg–Landau Equation via ExtendedHyperbolic Function Approach**The project supported by National Natural ScienceFoundation of China under Grant No. 10372094, the Natural ScienceFoundation of Zhejiang Province of China under Grant No. 102053, and the Foundation of Zhejiang Education Committee under Grant No. 20030706

Abstract

In this paper, we extend the hyperbolic function approach for constructing the exact solutions ofnonlinear differential-difference equation (NDDE) in a unifiedway. Applying the extended approach and with the aid of Maple, wehave studied the discrete complex Ginzburg–Landauequation (dCGLE). As a result, we find a set of exactsolutions which include bright and dark soliton solutions.