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Solitary Wave Solutions of Discrete Complex Ginzburg–Landau Equation by Modified Adomian Decomposition Method

In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg—Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.