Exact solutions of nonlinear differential equations are of great importance to the theory and
practice of complex systems. The main point of this review article is to discuss a specific …

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 …

The long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary
conditions at infinity is investigated by the nonlinear steepest descent method of Deift and …

We propose a modification of the standard inverse scattering transform for the focusing
nonlinear Schrödinger equation (also other equations by natural generalization) formulated …

We construct the multi‐breather solutions of the focusing nonlinear Schrödinger equation
(NLSE) on the background of elliptic functions by the Darboux transformation, and express …

In this work, the initial value problem of the nonlocal short pulse (NSP) equation is studied
with the Schwartz-type initial data. Our aim is to adequately study the long-time asymptotic …

In this paper, we report a rigorous theory of the inverse scattering transforms (ISTs) for the
derivative nonlinear Schrödinger (DNLS) equation with both zero boundary conditions …

Rogue waves are anomalously high waves that may suddenly form on the sea surface. At
the dawn of the 21st century, they attracted the interest of researchers, from oceanographers …

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of
weakly interacting solitons in the framework of Korteweg–de Vries (KdV) equation. In this …

We report an optical fiber experiment in which we study the nonlinear stage of modulational
instability of a plane wave in the presence of a localized perturbation. Using a recirculating …