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Space nonlinear localization can occur in perfectly periodic nonlinear arrays when the coupling between substructures is sufficiently weak. Under these assumptions, different nonlinear phenomena can arise such as solitary waves or solitons, which has been shown to be orbitally stable, and thus physically realizable. Several researches were devoted to study solitons in discrete systems such as pendulums, MEMS, granular crystals arrays where they are called Intrinsic Localized Modes (ILMs), Discrete Breathers (DBs) or lattice solitons. The prediction is an essential tool allowing researchers to select the accurate physical parameters, for which ILMs can occur to either localize energy or avoid it.

For this purpose, we introduce a general model of a damped and driven nonlinear weakly coupled oscillators array. The multiple scales method is employed allowing to transform the discrete system of coupled differential equations into the continuous damped and driven Nonlinear Schrödinger (NLS) equation. This later is solved analytically for zero damping, giving rise to two different soliton waves. Nonetheless, the damped system is solved numerically using the continuous analog of Newton’s method. Subsequently, numerical simulations were carried out in order to investigate the influence of physical parameters on the existence and stability of the soliton waves.