We show numerically the existence of vibrating soliton pairs that are consistent with observations performed with a passively mode-locked fiber laser. These vibrating pairs are new types of multisoliton complexes that exist in the vicinity of the phase-locked soliton pairs discovered a few years ago [Opt. Lett.27, 966 (2002)]. The pairs are found numerically with a laser propagation model that includes nonlinear dissipation and cavity periodicity, and they can appear following a Hopf-type bifurcation when a cavity parameter is tuned.
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