Abstract
A survey of recent theoretical and experimental studies on localized structures that form and propagate in a broad class of optical and matter-wave media is presented. The article is structured as a resource paper that overviews a large series of theoretical and experimental results obtained in diverse research areas: linear and nonlinear optical waveforms, nonlinear surface waves, ultrashort few-cycle optical pulses, localized structures in fractional systems, rogue (freak) waves, and matter-wave localized states.
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