We review the different dynamical mechanisms leading to the emergence of coherent
structures in physical systems described by the integrable one-dimensional nonlinear …

Dissipative solitons are remarkably localized states of a physical system that arise from the
dynamical balance between nonlinearity, dispersion and environmental energy exchange …

Modulation instability is a fundamental process of nonlinear science, leading to the unstable
breakup of a constant amplitude solution of a physical system. There has been particular …

The nonlinear Schrödinger equation is the standard model in nonlinear optics. The pulse
propagation in an isotropic medium can be described by this equation. This paper reports …

Optical fibres are favourable tabletop laboratories to investigate both coherent and
incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear …

An elegant method of nonlinear Fourier transform (NFT) has attracted worldwide research
interests and such NFT methodology provides a new viewpoint on the physics of laser …

We review the spectral theory of soliton gases in integrable dispersive hydrodynamic
systems. We first present a phenomenological approach based on the consideration of …

Soliton gases represent large random soliton ensembles in physical systems that exhibit
integrable dynamics at the leading order. Despite significant theoretical developments and …

Fiber lasers are a paradigm of dissipative systems, which distinguish themselves from a
Hamilton system where energy is conservative. Consequently, pulses generated in a fiber …

We report experimental confirmation of the universal emergence of the Peregrine soliton
predicted to occur during pulse propagation in the semiclassical limit of the focusing …