In this paper, we are concerned with the Riemann–Hilbert approach for the higher-order
Gerdjikov–Ivanov equation with nonzero boundary conditions. A uniformization variable will …

General soliton solutions to a nonlocal nonlinear Schrödinger (NLS) equation with PT-
symmetry for both zero and nonzero boundary conditions are considered via the …

In this paper, we present a systematical inverse scattering transform for both focusing and
defocusing nonlocal (reverse-space–time) modified Korteweg–de Vries (mKdV) equations …

We characterize the nonlinear stage of modulational instability (MI) by studying the longtime
asymptotics of the focusing nonlinear Schrödinger (NLS) equation on the infinite line with …

Nonlocal reverse space‐time Sine/Sinh‐Gordon type equations were recently introduced.
They arise from a remarkably simple nonlocal reduction of the well‐known AKNS scattering …

In this topical review paper we provide a survey of classical and more recent results on the
IST for one-dimensional scalar, vector and square matrix NLS systems on the line (-∞< …

We explore the inverse scattering transforms with matrix Riemann–Hilbert problems for both
focusing and defocusing modified Korteweg–de Vries (mKdV) equations with non-zero …

The any multi-component nonlinear Schrödinger (alias n-NLS) equations with nonzero
boundary conditions are studied. We first find the fundamental and higher-order vector …

Nonlocal reverse space–time equations of the nonlinear Schrödinger (NLS) type were
recently introduced. They were shown to be integrable infinite-dimensional dynamical …

The theory of inverse scattering is developed to study the initial-value problem for the matrix
modified Korteweg–de Vries (mKdV) equation with the 2 m× 2 m (m≥ 1) Lax pairs and finite …