The nonlinear Schrödinger equation has wide range of applications in physics with spatial
scales that vary from microns to kilometres. Consequently, its solutions are also universal …

The complex cubic-quintic Ginzburg–Landau equation (CQGLE) is a universal model for
describing a dissipative system, especially fiber laser. The analytic one-soliton solution of …

Doubly localized two-dimensional rogue waves for the Davey–Stewartson I equation in the
background of dark solitons or a constant, are investigated by employing the Kadomtsev …

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 …

Rogue wave patterns in the nonlinear Schrödinger equation are analytically studied. It is
shown that when an internal parameter in the rogue waves (which controls the shape and …

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 …

Optical fibers are used in the communications, biological sensors and chemical sensors. We
investigate a variable-coefficient modified Hirota equation for the amplification or absorption …

In this work, two approaches are introduced to solve a linear damped nonlinear Schrödinger
equation (NLSE) for modeling the dissipative rogue waves (DRWs) and dissipative …

We show that universal rogue wave patterns exist in integrable systems. These rogue
patterns comprise fundamental rogue waves arranged in shapes such as a triangle …