  This paper discusses about solutions of the nonlocal nonlinear Schrodinger
equation. We prove that the solution remains close to the orbit of the soliton
for a large-time, if the initial data is close to the ground state solitons.
The proof uses the hyperbolic dynamics near ground state, which exhibits
properties of local structural stability of solutions with respect to the flows
of the nonlocal nonlinear Schrodinger equation.
