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This paper investigates the existence of intersite soliton in the Ablowitz-Ladik-cubic discrete nonlinear Schrödinger (AL-cubic DNLS) equation in the anti-continuum limit by using a variational approximation (VA) method. The AL-cubic equation interpolates the integrable Ablowitz-Ladik DNLS equation and the non-integrable cubic DNLS equation. We obtain that the approximated solitons are in good agreement with those resulted from numerics. We also show that the approximated solitons are valid for small coupling constant and for the interpolation parameter in the vicinity of the cubic DNLS equation.     Keywords: Discrete Nonlinear Schrödinger equation, intersite soliton, Ablowitz-Ladik equation, variational approximation.

Variational Approximations for Intersite Soliton in a Ablowitz-Ladik-Cubic Discrete Nonlinear Schrödinger Equation