Vibrational spectrum of dissipative soliton molecules

The coexistence of a multiplicity of vibrational states in a fiber laser is demonstrated for a specific set of laser parameters. These vibrational states consist of two dissipative solitons, whose distance and/or relative phase change periodically. More complex vibrations, involving either commensurate or incommensurate frequencies, are also reported. The multiplicity of available vibrations anticipates a much more intricate scenario when more than two solitons are involved. The case with three solitons is also examined.