We present an overview of nonlinear phenomena related to optical quadratic solitons—
intrinsically multi-component localized states of light, which can exist in media without …

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of
research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and …

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 …

This monograph systematically develops and considers the so-called" dressing method" for
solving differential equations (both linear and nonlinear), a means to generate new non …

In this paper, we first modify the binary Darboux transformation to derive three types of
soliton interaction solutions of the Davey-Stewartson I equation, namely the higher-order …

General doubly localized two-dimensional lumps on a background of homoclinic orbits or
constant in the Davey–Stewartson I equation are studied. These special lumps first emerge …

The reductive perturbation method is a very powerful way of deriving simplified models
describing nonlinear wave propagation and interaction. In abstract frames chosen for the …

Under investigation in this work is the Davey–Stewartson (DS) II equation. Based on the
Kadomtsev–Petviashvili (KP) reduction method and Schur polynomial theory, we construct …

In this paper, we study the dynamics of an interesting class of vector solitons in the long-
wave–short-wave resonance interaction (LSRI) system. The model that we consider here …

A prototypical example of a rogue wave (RW) structure in a two-dimensional (2D) nonlocal,
nonlinear Schrödinger model, namely, a variant of the Benney-Roskes (BR) system, is …