Generalized Differential Transform Method for Solving Discrete Complex Cubic Ginzburg–Landau Equation

Abstract

In this paper, generalized differential transform method (GDTM) is applied to solve discrete complex cubic Ginzburg–Landau (DCCGL) equation which is a famous nonlinear difference-differential equation (NDDE). GDTM approximate solutions for various discrete soliton solutions of DCCGL such as discrete bright soliton, discrete dark soliton, and discrete alternating soliton are obtained. Also this method is successfully employed to obtain approximate solution for dark solitary wave solution of integrable discrete nonlinear Schrödinger (IDNS) equation. Numerical results compared with their corresponding numerical and analytical solutions to show the efficiency and high accuracy of the considered method.