Asymptotic behavior of small solutions to a 2-component system of cubic nonlinear Schrödinger equations in one space dimension

In this manuscript we specify asymptotic behavior of small solutions to initial value problem for a 2-component system of cubic nonlinear Schrödinger equations in one dimensional Euclidean space. As a consequence, the solution behaves like a free solution as $t\to +\infty$. Moreover, a non-decay result for the solution is derived, which is non-trivial in terms of the long range scattering.