Apart from parameter-invariant stationary solitons, numerous nonlinear systems support breathing dissipative solitons (DSs), manifesting themselves as nonlinear waves in which energy concentrates in a localized and oscillatory fashion. In this talk, we review our recent results and advances on breathing DSs. By employing ultrafast laser setups whose outputs are spectrally and temporally analysed in real time, we unveil rich dynamics of breathing DSs in mode-locked fibre lasers. These include establishes a general, deterministic route to induce breathing DSs in normal-dispersion mode-locked fibre lasers, the observation of breather explosions, breather molecules, and molecular complexes in fiber lasers. Numerical simulations based on the complex Ginzburg-Landau equation confirm our experimental observations. These results not only carry significance from an application perspective, but also contribute more broadly to the fundamental understanding of dissipative soliton physics.
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