Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media

We introduce a class of spatial complex-variable-function Gaussian (CVF Gaussian) beams, which are the product of an arbitrary analytic complex variable function and a Gaussian function, in strongly nonlocal nonlinear media (SNNM). The CVF Gaussian beam rotates generally during propagation. By choosing the input power of the beam, we can obtain a CVF Gaussian breather or a CVF Gaussian soliton. We reveal that a stable CVF Gaussian beam can exist in SNNM with different forms, including rotating dipoles, rotating elliptic doughnuts, and rotating figure eights.