The　propagation　and　imaging　of　two　orthogonally　polarized　Gaussian　optical　beams　passing　through　a　nonlinear　graded-index　rod　lens　are　analyzed　using　a　variational　approach,　and　it　is　concluded　that　there　are　two　regimes　of　propagation,　collapse　and　oscillation.　The　results　show　that　the　nonlinear　interaction　of　two　optical　beams　has　great　effects　on　the　propagation　and　imaging　characteristics　of　optical　beams,　and　that　one　beam　can　control　the　propagation　and　imaging　of　the　other　beam.