  We propose a novel model which efficiently describes the magnetization
dynamics in a magnetic bilayer system. By applying a particular gauge
transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully
convert the model into an exactly integrable framework. Thus the obtained
analytical solutions allows us to predict a 1D magnetic soliton pair existed by
tunning the thickness of the spacing layer between the two ferrimagnetic
layers. The decoupling-unlocking-locking transition of soliton motion is
determined at various interaction intensitiy. Our results have implications for
the manipulation of magnetic solitons and the design of magnetic soliton-based
logic devices.
