In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typically non-variational Slonczewski term. Taking axial symmetry into account, we study the existence of domain wall type coherent structure solutions, with focus on one space dimension and spin-polarization, but our results also apply to vanishing spin-torque term. Using methods from bifurcation theory for arbitrary constant applied fields, we prove the existence of domain walls with nontrivial azimuthal profile, referred to as inhomogeneous. We present an apparently new type of domain wall, referred to as non-flat, whose approach of the axial magnetization has a certain oscillatory character. Additionally, we present the leading order mechanism for the parameter selection of flat and non-flat inhomogeneous domain walls for an applied field below a threshold, which depends on anisotropy, damping, and spin-transfer. Moreover, numerical continuation results of all these domain wall solutions are presented. * Universität Bremen, lars.siemer@uni-bremen.de; Corresponding author † Universität Hamburg ‡ Universität Bremen 2 Model equations and coherent structure formThe classical model for magnetization dynamics was proposed by Landau and Lifschitz based on gyromagnetic precession, and later modified by Gilbert [15, 16]. See [17] for an overview. The Landau-Lifschitz-Gilbert equation for unit vector fields m(x, t) ∈ S 2

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This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non-variational Slonczewski term for spin-torque effects. Taking applied field and spin-polarization as the primary parameters, we study dynamic stability as well as selection mechanisms analytically and numerically in an axially symmetric setting. Concerning the stability of the DWs' asymptotic states, we distinguish the bistable (both stable) and the monostable (one unstable, one stable) parameter regime. In the bistable regime, we extend known stability results of an explicit family of precessing solutions and identify a relation of applied field and spin-polarization for standing DWs. We verify that this family is convectively unstable into the monostable regime, thus forming so-called pushed fronts, before turning absolutely unstable. In the monostable regime, we present explicit formulas for the so-called absolute spectrum of more general matrix operators. This allows us to relate translation and rotation symmetries to the position of the singularities of the pointwise Green's function. Thereby, we determine the linear selection mechanism for the asymptotic velocity and frequency of DWs and corroborate these by long-time numerical simulations. All these results include the axially symmetric Landau-Lifschitz-Gilbert equation.

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