Solitons are large-amplitude, spatially confined wave packets in nonlinear media. They occur in a wide range of physical systems, such as water surfaces, optical fibres, plasmas, Bose–Einstein condensates and magnetically ordered media1,2. A distinguishing feature of soliton behaviour that is common to all systems, is that they propagate without a change in shape owing to the stabilizing effect of the particular nonlinearity involved1,3. When the propagation path is closed, modes consisting of one or several solitons may rotate around the ring, the topology of which imposes additional constraints on their allowed frequencies and phases4,5. Here we measure the mode spectrum of spin-wave solitons in a nonlinear active ring constructed from a magnetic ferrite film. Several unusual symmetry-breaking soliton-like modes are found, such as ‘Möbius’ solitons, which break the fundamental symmetry of 2π-periodicity in the phase change acquired per loop: a Möbius soliton needs to travel twice around the ring to meet the initial phase condition.
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Remoissenet, M. Waves Called Solitons: Concepts and Experiments (Springer, Berlin/Heidelberg, 1994)
Khaykovich, L. et al. Formation of a matter-wave bright soliton. Science 296, 1290–1293 (2002)
Agrawal, G. P. Nonlinear Fiber Optics (Academic, San Diego, 1995)
Carr, L. D., Clark, C. W. & Reinhardt, W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62, 063610 (2000)
Carr, L. D., Clark, C. W. & Reinhardt, W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity. Phys. Rev. A 62, 063611 (2000)
Liu, X., Qian, L. J. & Wise, F. W. Generation of optical spatiotemporal solitons. Phys. Rev. Lett. 82, 4631–4634 (1999)
Bauer, M. et al. Observation of spatiotemporal self-focusing of spin waves in magnetic films. Phys. Rev. Lett. 81, 3769–3772 (1998)
Kivshar, Y. S. & Malomed, B. A. Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61, 763–915 (1989)
Li, Z., Li, L., Tian, H., Zhou, G. & Spatschek, K. H. Chirped femtosecond solitonlike laser pulse form with self-frequency shift. Phys. Rev. Lett. 89, 263901 (2002)
Kalinikos, B. A., Scott, M. M. & Patton, C. E. Self-generation of fundamental dark solitons in magnetic films. Phys. Rev. Lett. 84, 4697–4700 (2000)
Kalinikos, B. A., Kovshikov, N. G., Kostylev, M. P. & Benner, H. Self-generation of spin-wave envelope soliton trains with different periods. JETP Lett. 76, 253–257 (2002)
Kalinikos, B. A., Kovshikov, N. G. & Patton, C. E. Self-generation of microwave magnetic envelope soliton trains in yttrium iron garnet thin films. Phys. Rev. Lett. 80, 4301–4304 (1998)
Steinmeyer, G., Sutter, D. H., Gallmann, L., Matuschek, N. & Keller, U. Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics. Science 286, 1507–1512 (1999)
Bagada, A. V., Melkov, G. A., Serga, A. A. & Slavin, A. N. Parametric interaction of dipolar spin wave solitons with localized electromagnetic pumping. Phys. Rev. Lett. 79, 2137–2140 (1997)
Kolodin, P. A. et al. Amplification of microwave magnetic envelope solitons in thin yttrium iron garnet films by parallel pumping. Phys. Rev. Lett. 80, 1976–1979 (1998)
Melkov, G. A. et al. Nonadiabatic interaction of a propagating wave packet with localized parametric pumping. Phys. Rev. E 63, 066607 (2001)
Nash, J. M., Kabos, P., Staudinger, R. & Patton, C. E. Phase profiles of microwave magnetic envelope solitons. J. Appl. Phys. 83, 2689–2699 (1998)
Support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also thank J.D. Comins for a careful reading of the manuscript.
The authors declare that they have no competing financial interests.
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Demokritov, S., Serga, A., Demidov, V. et al. Experimental observation of symmetry-breaking nonlinear modes in an active ring. Nature 426, 159–162 (2003). https://doi.org/10.1038/nature02042
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