Degenerate lump interactions within the Kadomtsev-Petviashvili equation

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 in media with positive dispersion. As has been established, lumps of equal amplitudes can experience anomalously slow interactions. They can also form stationary bound states - multilumps. The features of anomalous interactions of lumps and multilumps have not been studied yet in detail. Therefore, this work aims to find a simple and fast method to derive bound states of lumps and study anomalous interactions of multilumps. The asymptotic behaviour of lumps is analysed analytically and numerically, and the results obtained are illustrated graphically. The approach introduced in this paper can be generalised to other (2+1)-dimensional integrable systems. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the anomalous scattering of lumps within the Kadomtsev-Petviashvili equation. It is found that lumps of equal amplitudes can experience anomalously slow interactions and form stationary bound states. The asymptotic behavior of lumps is analyzed analytically and numerically, and the results are illustrated graphically. The approach introduced in this paper can be extended to other (2+1)-dimensional integrable systems.