Propagations of elliptic beams in nonlocal nonlinear media with linear anisotropy

Analytically discussed is the dynamical properties of the elliptic beams in nonlocal nonlinear media with linear anisotropy. The exact elliptic soliton solutions are obtained for the Snyder-Mitchell model with linear anisotropy in the case of the strong nonlocality. The ellipticity of the elliptic solitons is equal to the square root of the anisotropy parameter of the media with linear anisotropy. When the input optical powers depart from the soliton powers, the elliptic beams are shown by us to have two dynamical behaviors, the optical breathers for the case that the anisotropy parameter of the media is a rational number, and pseudo breathers for the case that the anisotropy parameter is an irrational number, where pseudo breathers are referred to as the dynamical states that the elliptic beams after propagations cannot recover their initial shapes, although both the two semi-axes of the elliptic beams evolve periodically. The analytical solutions agree well with the numerical simulations.