A model which is proposed by JUNG P S et al. is employed to demonstrate analytically properties of individual bright solitons in liquid crystals with competing nonlinearities under the condition of unequal nonlocality of the thermal effect and the reorientational effect. The evolution of the parameters, such as amplitude, width, chirp and phase with transmission distance, are obtained by the variational method. The amplitude and width are closely related to the beam power. The beam width decreases monotonously with the increase of thermal nonlocality and increases monotonously with the increase of thermal nonlinearity. In this case, the equivalent potential which is relate the power of the beams is also obtained. It is predicted by the potential that the larger the incident beam power is, the smaller the bright soliton width is. It is obtained by the variational method that the beam width oscillates periodically with the transmission distance when the incident power is 4 or 8. There are obvious differences between the two oscillation trends. When the power is 4, the width of the beam is always greater than or equal to the initial width. When the power is 8, the width of the beam is always less than or equal to the initial width. The variation of beam width with transmission distance is consistent with the numerical simulation results.