Gaussian lossy spatial soliton in strongly nonlocal media

The propagation property of 1+1 dimensional Gaussian optical beam is investigated in small lossy strongly nonlocal nonlinear media by means of variational method. The evolution equations of the parameters, the beam width evolution law and a critical power are obtained for the beam. In the case of small loss, a lossy optical spatial soliton with beam width slow diffraction is found when the input power equals the critical power. When the input power is smaller than the critical power, the beam width takes quasi-periodical diffraction with the Jacobian elliptic sine and elliptic cosine functions. When the input power is larger than the critical power, it changes from quasi-periodical contraction to diffraction with the same functions.