Pulse propagation in optical fibers may electrostrictively excite acoustic waves as a result of cladding Brillouin scattering, transversally propagating with respect to the fiber axis in the fiber's cladding, and mechanical coating. We show, for the first time to our knowledge, experimentally and theoretically that these transverse resonances within finite frequency ranges may cooperatively couple with the acoustic longitudinal modes of a fiber resonator, giving rise to stable trains of either spread or compressed three-wave Brillouin solitons and propose a first stability map for the rich four-wave dissipative dynamics.
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