Based on the Snyder-Mitchell model that describes the paraxial beam propagating in strongly nonlocal nonlinear media and the trial solution with modulating the Gaussian beam by the parabolic cylinder functions, the close forms of elegant Hermite-Gaussian beams (EHGB) are accessed in Cartesian coordinate system. The collinear EHGB will evolve to be the rotating charge vortex EHGB on certain condition. It is shown that the transferring of the single EHGB and the rotating charge vortex EHGB at the critical power. The widths of the profiles of the breathers and the rotating charge vortex breathers are varied periodically in the transferring.