Resonant collisions among localized lumps and line solitons of the Kadomtsev–Petviashvili I
(KP‐I) equation are studied. The KP‐I equation describes the evolution of weakly nonlinear …

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 …

The interaction of two lump solitons described by the Kadomtsev–Petviashvili I (KPI)
equation is analysed using both exact and numerical methods. The numerical method is …

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 …

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 …

Based on the Hirota bilinear form of the KP equation, five classes of interaction solutions
between lumps and line solitons are generated via Maple symbolic computations. Analyticity …

We construct a broad class of solutions of the Kadomtsev–Petviashvili (KP)‐I equation by
using a reduced version of the Grammian form of the‐function. The basic solution is a linear …

In most cases, the lump wave will collide with line waves and breather waves in the hybrid
solutions for (2+ 1)-dimensional integrable systems. However, this study introduces a new …

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII)
equation by investigating the Wronskian form of its tau-function. We show that, in addition to …

The simplified form of the Hirota's method is used to handle a generalized (3+ 1)-
dimensional Kadomtsev–Petviashvili (KP) equation. Multiple-soliton solutions and multiple …