Dissipative soliton dynamics of the Landau–Lifshitz–Gilbert equation

We study ferromagnetic dissipative systems described by the isotropic LLG equation, from the standpoint of their spatially localized dynamical excitations. In particular, we focus on dissipative soliton solutions of a nonlocal NLS equation to which the LLG equation is transformed and use Melnikov's theory to prove the existence of these solutions for sufficiently small dissipation. Next, we employ pseudospectral and PINN (physics-informed neural network) numerical techniques of machine learning to demonstrate the validity of our analytic results. Such localized structures have been detected experimentally in magnetic systems and observed in nano-oscillators, while dissipative magnetic droplet solitons have also been found theoretically and experimentally.