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 …

A formulation of Darboux transformations is proposed for integrable couplings, based on
non-semisimple matrix Lie algebras. Applications to a kind of integrable couplings of the …

We perform a survey of some recent theoretical and experimental studies on
multidimensional (two-and three-dimensional) localized structures in optical and matter …

This review is dedicated to recent progress in the active field of rogue waves, with an
emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector …

Recently, the physics-informed neural networks (PINNs) have received more and more
attention because of their ability to solve nonlinear partial differential equations via only a …

In this research, based on Darboux transformation, a molecule consisting of two identical
soliton waves is firstly obtained by velocity resonance for modified KdV equation. And we …

In this paper, we provide a generating mechanism to obtain rogue wave solutions from N
soliton of Hirota's bilinear method. Based on the long wave limit method, the phase …

Based on Darboux transformation, we generate breather solutions sitting on zero
background via module resonance for complex modified KdV equation. Then, some novel …

We construct an analytical and explicit representation of the Darboux transformation (DT) for
the Kundu–Eckhaus (KE) equation. Such solution and n-fold DT T n are given in terms of …

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries
(mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915–946 (2016)] …