based on the normalized spatiotemporal lugiato-lefever equation, the evolutions of cosine-modulated stationary fields relating to the generation of single-free spectral range (fsr) or multi-fsr kerr frequency combs in a microresonator with anomalous dispersion are studied numerically. the research results show that a single-fsr comb arises when a dissipative soliton pulse or multiple nonequidistant soliton pulses form in the cavity. compared with the smooth and regular spectral structure of a single soliton pulse, the comb corresponding to the uneven distribution of multiple soliton pulses exhibits a complex and irregular profile. when the stable intracavity field consists of a "roll" turing pattern or n(n > 1) evenly distributed soliton pulses separated by 2 pi/n, multi-fsr combs can be generated. in the case of the "roll" turing pattern solution, it is found that third-order dispersion could modify the comb mode spacing and decrease the intensity of high-order comb modes. for the situation of multiple soliton pulse generation, the simulation results indicate that both the number and locations of the soliton pulses can be actively controlled through the careful selection of modulation frequency. in addition, for the selected cosine-modulated initial field profile, only those modes with the mode numbers being equal to an integer multiple of n can be greatly amplified by the parametric gain during propagation in the microresonator. this process eventually leads to the formation of a n-fsr frequency comb. (c) 2015 optical society of america