Breather bound states in a parametrically driven magnetic wire

TL;DR

This paper systematically investigates localized dynamical states, including breathers and solitons, in a parametrically driven magnetic wire modeled by the Landau-Lifshitz-Gilbert equation, revealing multistability and complex dynamics.

Contribution

It introduces a comprehensive analysis of localized states in a driven magnetic wire, identifying stability regions and dynamical behaviors using simulations of the LLG equation.

Findings

Existence of stable single- and multi-soliton states.

Observation of breather emission and drift due to symmetry breaking.

Identification of regular and chaotic dynamics via Lyapunov exponents.

Abstract

We report the results of systematic investigation of localized dynamical states in the model of a one-dimensional magnetic wire, which is based on the Landau-Lifshitz-Gilbert (LLG) equation. The dissipative term in the LLG equation is compensated by the parametric drive imposed by the external AC magnetic field, which is uniformly applied perpendicular to the rectilinear wire. The existence and stability of the localized states is studied in the plane of the relevant control parameters, viz., the amplitude of the driving term and the detuning of its frequency from the parametric resonance. With the help of systematically performed simulations of the LLG equation, existence and stability areas are identified in the parameter plane for several species of the localized states: stationary single- and two-soliton modes, single and double breathers, drifting double breathers with spontaneously broken inner symmetry, and multi-soliton complexes. Multistability occurs in this system. The breathers emit radiation waves (which explains their drift caused by the spontaneous symmetry breaking, as it breaks the balance between the recoil from the waves emitted to left and right), while the multi-soliton complexes exhibit cycles of periodic transitions between three-, five-, and seven-soliton configurations. Dynamical characteristics of the localized states are systematically calculated too. These include, in particular, the average velocity of the asymmetric drifting modes, and the largest Lyapunov exponent, whose negative and positive values imply that the intrinsic dynamics of the respective modes is regular or chaotic, respectively.