In this work, we employ the∂¯-steepest descent method to investigate the Cauchy problem
of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space …

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 …

The main attention of this study is focused on the interaction dynamics of breather, and
hybrid solitons and breather for an extended generalization of Vakhnenko equation. The …

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 …

Abstract The Riemann–Hilbert (RH) problem is developed to study the focusing nonlinear
Schrödinger (NLS) equation with multiple high-order poles under nonzero boundary …

This paper is devoted to studying the second type of complete integrable complex Wadati–
Konno–Ichikawa-II (cWKI-II) equation. We first study the conservation laws and construct the …

Rogue waves in the nonlocal PT PT-symmetric nonlinear Schrödinger (NLS) equation are
studied by Darboux transformation. Three types of rogue waves are derived, and their …

Under investigation in this paper is the (4+ 1)-dimensional nonlinear Fokas equation, which
is an important physics model. With the aid of Bell's polynomials, an effective and …

General rogue waves are derived for the generalized derivative nonlinear Schrödinger
(GDNLS) equations by a bilinear Kadomtsev–Petviashvili (KP) reduction method. These …

We analyze the large-n behavior of soliton solutions of the integrable focusing nonlinear
Schrödinger equation with associated spectral data consisting of a single pair of conjugate …