A rigorous theory of the inverse scattering transform for the defocusing nonlinear
Schrödinger equation with nonvanishing boundary values as is presented. The direct …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

We first reveal that there is a Riccati-type Miura transformation from the Fokas–Lenells (FL)
system to the first member of the negative part of the AKNS hierarchy. We derive a vectorial …

General soliton solutions to a reverse‐time nonlocal nonlinear Schrödinger (NLS) equation
are discussed via a matrix version of binary Darboux transformation. With this technique …

The paper is to reveal the direct links between the well known Sylvester equation in matrix
theory and some integrable systems. Using the Sylvester equation KM+ MK= rs T we …

Multiple pole solutions consist of groups of weakly bound solitons. For the (focusing)
nonlinear Schrödinger equation the double pole solution was constructed by Zakharov and …

A Darboux transformation and general vector dark soliton solutions are constructed for multi-
component complex modified Korteweg–de Vries (mKdV) system. Dark soliton solutions …

We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV
hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in …

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of
equations are presented. The class corresponds to a Lax operator with entries in a …

We reveal the origin and structure of self-consistent source extensions of integrable
equations from the perspective of binary Darboux transformations. They arise via a …