Novel resonant soliton interactions for the Konopelchenko-Dubrovsky equation

This paper investigates the resonant soliton interactions for the (2+ 1)-dimensional Konopelchenko-Dubrovsky equation, a model that describes shallow water waves with weak nonlinear restoring forces. Through symbolic computation and asymptotic analysis, we make a comprehensive classification of the resonant interactions between two solitons. Such equation admits both bell-shaped solitons and kink solitons, and allows us to identify four distinct types of resonance interactions, expanding beyond the common two cases. A novel discovery is the resonant interaction between a bell-shaped soliton and a kink soliton, where the bell-shaped soliton transforms into a kink soliton, which has not been reported before. Detailed graphical analyses are presented, providing clear visual representations of the soliton behaviors and their dynamic interactions. The results obtained in this study offer new insights into the complexity of soliton dynamics in higher-dimensional nonlinear systems.