  The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and
indispensable framework within the realm of magnetism. However, solving the LLG
equation, encompassing full nonlinearity amidst intricate complexities,
presents formidable challenges. In this context, we develop a precise mapping
through geometric representation, establishing a direct linkage between the LLG
equation and an integrable generalized nonlinear Schr\"odinger equation. This
novel mapping provides accessibility towards acquiring a great number of exact
spatiotemporal solutions. Notably, exact chiral magnetic solitons, critical for
stability and controllability in propagation with and without damping effects
are discovered. Our formulation provides exact solutions for the long-standing
fully nonlinear problem, facilitating practical control through spin current
injection in magnetic memory applications.
