Lump–soliton, rogue–soliton interaction solutions of an evolution model for magnetized Rossby waves

In this study, a fluid mechanics model (2 + 1)-dimensional Kadomtsev–Petviashvili model with magnetic Rossby wave parameters is researched. Four sets interactions of the equation are obtained by applying symbolic calculation and polynomial functions, the polynomial functions are test functions about the first-order lump wave and the second-order rogue waves. We deduced the two theorems and got a couple of completely new paradigms. The two paradigms lead to two sets of the interactions among second-order rogue waves with solitons. Some diagrams were made to show the propagation properties of interaction waves. An interesting conclusion that when interacting with multiple exponential functions, lump and rogue are swallowed and fusion phenomena occurs as time goes on, when interacting with hyperbolic cosine functions, lump and rogue transfer from right soliton to left soliton of the kink solitons.