Castro, Camilo JoséOrtega-Piwonka, IgnacioMalomed, Boris A.Urzagasti, DeterlinoPedraja-Rejas, LilianaDíaz, PabloLaroze, David2024-11-282024-11-282024-11-22C. J. Castro, I. Ortega-Piwonka, B. A. Malomed, D. Urzagasti, L. Pedraja-Rejas, P. Díaz, D. Laroze. Symmetry 16(12), 1565 (2024)2073-8994https://hdl.handle.net/10115/42161Author Contributions Conceptualization, D.L.; Methodology, I.O.-P., B.A.M. and D.L.; Software, C.J.C., I.O.-P. and D.U.; Validation, C.J.C., I.O.-P., L.P.-R. and P.D.; Formal analysis, I.O.-P., B.A.M. and L.P.-R.; Investigation, C.J.C., I.O.-P., P.D. and D.L.; Data curation, C.J.C. and D.U.; Writing—original draft, C.J.C., I.O.-P. and B.A.M.; Writing-review and editing, B.A.M., L.P.-R., P.D. and D.L.; Visualization, C.J.C. and I.O.-P.; Supervision, B.A.M. and D.L.; Project administration, D.L. All authors have read and agreed to the published version of the manuscript. Funding The work of B.A.M. was supported, in part, by the Israel Science Foundation through grant No. 1695/22. P.D. and D.L. acknowledge partial financial support from FONDECYT 1231020. Data Availability Statement Data is contained within the article. Acknowledgments We thank Manuel J. Suazo from the University of Tarapacá for their valuable advice to implement the parallelization in our numerical algorithms. D.L. acknowledges the hospitality of Université Côte d’Azur (Nice, France) and Universidad Nacional de San Agustín (Arequipa, Perú), where part of this work was written. Conflicts of Interest The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript: LLG: Landau–Lifshitz–Gilbert PSD: Power Spectral Density LLE: Largest Lyapunov Exponent CM: Center of MassWe report the results of a 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, namely, 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, the 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 multisoliton 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 multisoliton 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.engAttribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/Landau-Lifshitz equationdispersive radiationsoliton dynamicsLyapunov exponentsmultistabilityinfo:eu-repo/semantics/article10.3390/sym16121565info:eu-repo/semantics/openAccess