Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

Rogue waves (RWs) are rare, extreme amplitude, localized wave packets, which have
received much interest recently in different areas of physics. Fiber lasers with their abundant …

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 …

In this paper, a coupled mixed derivative nonlinear Schrödinger system, which describes the
short pulses in the femtosecond or picosecond regime of a birefringent optical fiber, is …

In this work, we study an extended (2+ 1)-dimensional perturbed nonlinear Schrödinger
equation (P-NLS) with Kerr law nonlinearity in a nano optical fiber. The extended model …

Resonant collisions among localized lumps and line solitons of the Kadomtsev–Petviashvili I
(KP‐I) equation are studied. The KP‐I equation describes the evolution of weakly nonlinear …

We aim to construct a Liouville integrable Hamiltonian hierarchy from a specific matrix
spectral problem with four potentials through the zero curvature formulation. The Liouville …

Understanding the phenomenon of rogue wave formation, often called extreme waves, in
diverse branches of nonlinear science has become one of the most attractive domains …

Under investigation in this letter are the two-dimensional doubly localized rogue waves on a
background of dark solitons for the Fokas system, which are described by semi-rational …

The (2+ 1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations
describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using …