A survey of some 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 …

Breathers, modulation instability and recurrence phenomena are studied for the derivative
nonlinear Schrödinger equation, which incorporates second order dispersion, cubic …

Solitons are wave packets that can propagate without changing shape by balancing
nonlinear effects with the effects of dispersion. In photonics, they have underpinned …

We report recent results obtained with a novel optical fiber experimental setup based on a
heterodyne optical time-domain reflectometer in the context of FPU recurrence process …

In this paper, we construct rogue wave solutions on the periodic background for the fourth-
order nonlinear Schrödinger (NLS) equation. First, we consider two types of the Jacobi …

Nonlinear waves become asymmetric when asymmetric physical effects are present within
the system. One example is the self-steepening effect. When exactly balanced with …

Cross phase modulation (XPM) can induce soliton trapping in nonlinear medium, which has
been employed to achieve vector soliton, optical switching, and optical analog of gravity‐like …

In the present investigation, the breathers and rogue waves on the double-periodic
background are successfully constructed by Darboux transformation using a plane wave …

In this article, a new (2+ 1)-dimensional extension of the Hietarinta equation is proposed.
Two classes of lump and line rogue wave solutions are obtained for this equation by means …

Extreme events are rare and sudden abnormal deviations of the system's behavior from a
typical state. Statistical analysis reveals that if the time series contains extreme events, its …