Variational investigation of dipole solitons in nonlocal thermal media

A variational approach is presented to deal with the propagation of dipole solitons in nonlocal media with infinite range of nonlocality. And the oscillation of beamwidth is analyzed by a potential. When the potential function has zero at beamwidth W=1, the dipole soliton will form and could propagate stably at an appropriate input power with a profile of xexp(-x²/2) format. While the beamwidth would oscillate between a smallest and a maximum value when the input beam power does not equal to the soliton power. What is verified by the numerical simulations and results show that the input dipole beam would propagate with a periodic or quasi-periodic manner.