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 …

We report an optical fiber experiment in which we investigate the interaction between an
individual soliton and a dense soliton gas. We evidence a refraction phenomenon where the …

The mathematical description of localized solitons in the presence of large‐scale waves is a
fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear …

The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-
contained description of the periodic traveling wave solutions and Whitham modulation …

The question of whether features and behaviors that are characteristic to completely
integrable systems persist in the transition to non-integrable settings is a central one in the …

In this paper, on the background of general periodic travelling wave solutions, we construct
rogue wave solutions of the fifth-order Ito equation. In particular, those solutions cover the …

The long-time asymptotic behavior of solutions to the focusing nonlinear Schrödinger (NLS)
equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the …

In this work, we use the inverse scattering transform method to consider the focusing Kundu–
Eckhaus (KE) equation with nonzero background (NZBG) at infinity. Based on the analytical …

Rarefaction waves and dispersive shock waves are generated from the step-like initial data
in many nonlinear evolution equations including the classical example of the Korteweg–de …

The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is
analyzed using the Kadomtsev–Petviashvili II (KPII) equation. Building upon previous …