We propose a novel, analytically tractable, scenario of the rogue wave formation in the
framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the …

We investigate three-wave resonant interactions through both the generalized Darboux
transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark …

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are
investigated. We first explore the conditions for modulational instability of continuous waves …

In this work, we numerically consider the initial value problem for nonlinear Schr\" odinger
(NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian …

We study integrable coupled nonlinear Schrödinger equations with pair particle transition
between components. Based on exact solutions of the coupled model with attractive or …

Under investigation is a higher-order coupled Ablowitz–Ladik equation whose integrability is
established in the sense of Lax pair. With symbolic computation, the N-fold Darboux …

We study the (1+ 1) focusing nonlinear Schrödinger equation for an initial condition with
compactly supported parabolic profile and phase depending quadratically on the spatial …

A sampling approximation for a function defined on a bounded interval is proposed by
combining the Coiflet-type wavelet expansion and the boundary extension technique. Based …

The semiclassical (small dispersion) limit of the focusing nonlinear Schrödinger equation
with periodic initial conditions (ICs) is studied analytically and numerically. First, through a …

Nonlinear interactions in focusing media between traveling solitons and the dispersive
shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear …