Sasa–Satsuma type matrix integrable hierarchies are generated from taking two group
reductions of replacing the spectral parameter with its complex conjugate and its negative in …

Searching for higher-dimensional integrable models is one of the most significant and
challenging issues in nonlinear mathematical physics. This paper aims to extend the classic …

Study of the water waves remains central to fluid physics, ocean dynamics, and engineering.
In this paper, a (3+ 1)-dimensional extended shallow water wave equation is investigated …

Investigations into the nonlinear phenomena in fluid mechanics are of interest. In this paper,
we study an extended (2+ 1)-dimensional Kadomtsev-Petviashvili equation in fluid …

We show that complex higher-order lump patterns can be constructed in two different ways
within the Kadomtsev–Petviashvili (KP1) equation which describes nonlinear wave …

We present two different paths to degenerate normally interacting lump chains into
anomalously interacting lump patterns within the Kadomtsev–Petviashvili (KP1) equation. In …

We consider the anomalous scattering of lumps–fully localised two-dimensional solitary
waves–within the framework of the Kadomtsev–Petviashvili equation. Such entities can exist …

Under investigations in this paper are the bright solitons on the zero and periodic wave
background in the space-shifted PT-symmetric nonlocal nonlinear Schrödinger equation …

The focus of this paper is on the dynamics of degenerate and non-degenerate vector
solitons and their collision scenarios in the two-component long-wave–short-wave (2-LS) …

Using the Hirota bilinear method, we derive resonant solutions to the KP1 equation.
Solutions describe lump chains differently oriented in (x, y)-plane. We show that resonant …