Homoclinic Orbits and Localized Solutions in Discrete Nonlinear Schrodinger Equation with Long-Range Interaction

Document Type : Research Paper


1 Department of Mathematics and Informatics, Faculty of Exact Sciences, Natural and Life Sciences, El Arbi Tebessi University, Tebessa, Algeria.

2 Department of Mathematics and Informatic, Abdelhafidh Boussouf University Center of Mila, Mila, Algeria


In this paper, we use the homoclinic orbit approach without using small perturbations to prove the existence of soliton solutions of the discrete nonlinear Schrödinger 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.