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 …

Studies of the shallow water waves are active, possessing the applications in ocean
engineering, marine environment, atmospheric science, etc. In this paper, we investigate a …

Water waves can be seen in the rivers, lakes, oceans, etc. A (2+ 1)-dimensional Hirota–
Satsuma–Ito system, which arises in the shallow water waves, is investigated in this work …

A large member of lump chain solutions of the (2+ 1)-dimensional Bogoyavlenskii–
Kadomtsev–Petviashvili (BKP) equation are constructed by means of the τ-function in the …

Abstract The Kadomtsev–Petviashvili equation used in this article is used to model shallow
water waves with weakly nonlinear restorative forces as well as waves in a strong magnetic …

Resonant collisions of lumps with periodic solitons of the Kadomtsev–Petviashvili I equation
are investigated in detail. The usual lump is a stable weakly localized two-dimensional …

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 …

In this paper, the space-curved resonant solitons of the (2+ 1)-dimensional Ito equation are
constructed by means of a new constraint of the parameters of the N-solitons. The …

Constructing the exact solutions of high-dimensional nonlinear evolution equations and
exploring their dynamics have always been important and open problems in real-world …

Pattern formation in higher-order lumps of the Kadomtsev–Petviashvili I equation at large
time is analytically studied. For a broad class of these higher-order lumps, we show that two …