Exotic Coherent Structures and Their Collisional Dynamics in a (3+1) dimensional Bogoyavlensky-Konopelchenko Equation

TL;DR

This paper explores complex wave structures in a (3+1)D nonlinear equation, revealing unique elastic collision behaviors and hybrid phenomena not seen in lower dimensions, using Painlevé truncation for solution construction.

Contribution

It introduces new solutions for the (3+1)D Bogoyavlensky-Konopelchenko equation and uncovers novel collision dynamics and hybrid structures.

Findings

Line lumps undergo elastic collisions without energy exchange.

Hybrid dromions retain amplitude during interactions.

Discovery of nonparallel ghost solitons intersecting to form hybrid dromions.

Abstract

In this paper, we analyse the (3+1) dimensional Bogoyavlensky - Konopelchenko equation. Using Painlev\'e Truncation approach, we have constructed solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the solution, we have generated physically interesting solutions like periodic solutions, kinks, linear rogue waves, line lumps, dipole lumps and hybrid dromions. It is interesting to note that unlike in (2+1) dimensional nonlinear partial differential equations, the line lumps interact and undergo elastic collision without exchange of energy which is confirmed by the asymptotic analysis. The hybrid dromions are also found to retain their amplitudes during interaction undergoing elastic collision. The highlight of the results is that one also observes the two nonparallel ghost solitons as well whose intersection gives rise to hybrid dromions, a phenomenon not witnessed in (2+1) dimensions.