Abstract
In this paper, we use the homoclinic orbit approach without using small perturbations to prove the existence of soliton solutions of the discrete nonlinear Schrodinger equations with long-range interaction by employing the properties of the symmetries of reversible planar maps. Moreover, the long-range interaction by a potential proportional to $1/l^{1+alpha} $ with fractional $alpha < 1 $ and $l $ as natural number.
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