Variational solutions for Hermite--Gaussian solitons in nonlocal nonlinear media

The physical features exhibited by Hermite--Gaussian (HG) beamspropagating in nonlocal nonlinear media with Gaussian-shapedresponse are discussed with an approximate variational method. Usingdirect numerical simulations, we find that the beam properties inthe normalized system are different with the change of the degree ofnonlocality. It is shown that initial HG profiles break up intoseveral individual beams with propagation when the degree ofnonlocality $alpha$ is small. HG beams can propagate stably when$alpha$ is large enough.