Interaction and motion of multiple solitons in passively-mode-locked (PML) fiber lasers are investigated numerically. Three types of relative motions of two solitons are found in PML fiber lasers. The numerical results show that the relative motion of solitons attributes to the phase shift, which corresponds to the instantaneous frequency at pulse peak to be nonzero. Different from the classical dynamics of billiard balls, the interaction of solitons is similar to the Feynman diagram which is a pictorial way to represent the interaction of particles. After solitons interact with one another, their shapes do not change, but their phases shift and relative motions change. The theoretical results demonstrate that the separation of neighboring solitons in the laser cavity is about several hundred picoseconds to several nanoseconds. The theoretical predictions are in good agreement with the experimental results.
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