  We consider nonlinear Schr\"{o}dinger equation with strong magnetic fields in
3D. This model was derived by R L. Frank, F. M\'{e}hats, C. Sparber in 2017. We
prove modified scattering for small initial data and the existence of modified
wave operator for small final data. To describe asymptotic behavior of the NLS
we use the time-averaged model which was derived by the same authors as "the
strong magnetic confinement limit" of the NLS. We construct asymptotic
solutions which satisfy both asymptotic in time evolution and convergence in
the strong magnetic confinement limit. We also analyze the error between the
solution to the NLS and the time-averaged model for the same initial data and
obtain global estimates.
