Elliptic Hermite-Gaussian soliton in anisotropic strong nonlocal media

The propagation of elliptic Hermite-Gaussian (HG) beam in strong nonlocal media with elliptic Gaussian-shaped response function was studied by variational approach as well as numerical simulate. The evolution equations of the beam widths in x- and y-directions are obtained and the elliptic HG soliton is found. For forming such a soliton, the ratio of the square of the beam width must be proportional to the ratio of the characteristic length of the material, and the initial power should be equal to the two critical powers in x- and y-directions. For the anisotropic nonlinearity of the media, the instability of the high-order elliptic HG beam is increase as the increase of the order.