We consider the one-dimensional Landau–Lifshitz–Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous ini...

We demonstrate unusual features of phase dynamics, IV-characteristics and magnetization dynamics the $\varphi_0$ Josephson junction at small values spin-orbit interaction, ratio to magnetic energy Gilbert damping. In particular, an anomalous shift ferromagnetic resonance frequency with increase damping is found. The curves show Duffing oscillator behaviour, reflecting nonlinear nature Landau-Li...

Sets and Intervals • An interval with round brackets such as (a, b) means all the numbers between a and b not including a and b. We call this interval an open interval. • An interval with square brackets such as [a, b] means all the numbers between a and b including a and b. We call this interval a closed interval. • An interval with one square bracket and one closed bracket is called a clopen ...

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of GinzburgLandau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear...