[en] This paper presents new results obtained recently on theoretical investigations of self-focusing and filamentation in laser-plasma interactions. The filamentation instability, especially the competition among the filaments in the developing process, has been studied in detail for a more realistic nonuniform plasma. The authors find for the first time that development of the small perturbations is closely related to their initial phases θ. Calculations show that the small perturbations with different initial phases have different growth or decay rates. The small perturbations with θ > 0 will grow; those with θ < 0, however, will decay. This is a significant result, since it presents the possibility that, if they can control the initial phases of the small perturbations in experiments, the filamentation instability may be suppressed. Results also indicate that if the incident electromagnetic wave is linearly polarized, the light field in a developed filament will be linearly polarized in the same direction, which is in agreement with experimental observations