In this paper, we systematically investigate the nonlocal Hirota equation with nonzero
boundary conditions via Riemann–Hilbert method and multi-layer physics-informed neural …

Doubly localized two-dimensional rogue waves for the Davey–Stewartson I equation in the
background of dark solitons or a constant, are investigated by employing the Kadomtsev …

Based on the robust inverse scattering method, the high-order rogue wave of generalized
nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only …

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

Under investigation in this letter are the two-dimensional doubly localized rogue waves on a
background of dark solitons for the Fokas system, which are described by semi-rational …

The double-periodic solutions of the focusing nonlinear Schrödinger equation have been
previously obtained by the method of separation of variables. We construct these solutions …

The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is
constructed through the loop group method. The DT is then utilized to construct various …

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 …

It is shown how to compute the instability rates for the double-periodic solutions to the cubic
NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function …

In this paper, we address the Painlevé asymptotics of the solution in two transition regions
for the defocusing nonlinear Schrödinger (NLS) equation with finite density initial data iqt+ q …