The equation of motion for the coupled cavities of additive-pulse mode locking is solved with the eigenvalue method. The pulse evolution and self-starting condition for passive operation is analyzed. It is shown that the laser configuration is equivalent to an intracavity interferometer and a phase modulation across the pulse is the essential element for the mode locking. With the method developed, transient pulse evolution of an initial seed pulse can be calculated and thereby optimized. It is found that the pulse shortening rate is linear with respect to the number of round trips. The duration for the initial pulse to shorten to steady state is proportional to its initial width and inversely proportional to the nonlinear coefficient. The effect of dynamic gain saturation on the self-starting condition is also analyzed. The result shows that it would be difficult to achieve self-starting additive-pulse mode locking in the color-center and dye lasers due to their large emission cross sections. Single-cavity configurations of additive-pulse mode locking are proposed. It is shown that they are mathematically equivalent to the coupled-cavity one.