Elastic and resonant interactional solutions of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

In this paper, by using the Hirota bilinear method, we investigate elastic and resonant interactional solutions for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation, which is a fundamental model equation governing diverse nonlinear phenomena in fluid dynamics, plasma physics, nonlinear optics and so on. The introduced logarithmic transformation with a function of y facilitates the creation of more intricate and adaptable solution frameworks. We study three different cases of soliton interactions: the interactions between one breather and one kink soliton, the interactions between one breather and two kink solitons, and the interactions between two breathers. Through comprehensive asymptotic analysis and graphical representations, we elucidate the dynamic characteristics and fundamental properties of these nonlinear wave solutions. These solutions could uncover some novel nonlinear interactional patterns and shed light on the theoretical comprehension for the localized wave dynamics in higher-dimensional nonlinear systems.