Variational approach to beam propagation in nonlocal Kerr media

The beam propagation in nonlocal Kerr media is modeled by the nonlocal nonlinear Schrodinger equation. This problem can be re-interpreted with the variational approach. In the case of strong nonlocality, the response function can be expanded in Taylor's series, so that the variational problem can be found in a closed form. The evolution of the beam width can be obtained qualitatively by analysing the potential function. By means of a Reyleigh-Ritz optimization procedure, the closed form solutions for the evolution of beams in both defocusing and self-focusing cases can be obtained. When the beam propagates in a self-focusing material and its input power reaches a critical value, its width becomes fixed. The comparison with analytical solutions obtained by other approaches shows that the va