Abstract
The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons (magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
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Bethuel, F., Brezis, H. and Helein, F., 1994. Ginzburg-Landau Vortices. Boston, Birkhauser.
De Gennes, P. G. and Prost, J., 1993. The Physics of Liquid Crystals. Second Edition, (Oxford Science Publication), Clarendon Press, Oxford.
Fetter, A. L. and Svidzinsky, A. A., 2002. Vortices in Traped Dilute Bose-Einstein Condensates. Preprint.
Hang, F. B. and Lin, F. H., 2001. Static theory for planar ferromagnets and antiferromagnets.Acta Math. Sinica (Eng. ser.),17: 541–580.
Hang, F. B. and Lin, F. H., 2002. Travelling Wave Solutions of Schrödinger Map Equation. Preprint.
Huebener, R. P., 1979. Magnetic Flux Structures in Superconductors. Springer series in solid- state sciences, Springer Berlin.
Jaffe, A. and Taubes, C. H., 1980. Vortices and Monopoles. Birkhäuser, Boston.
Komineas, S. and Papanicolaou, N., 1996. Topology and dynamics in ferromagnetic media.Phys. D.,99: 81–107.
Lin, F. H. and Xin, J., 1999. On the incompressible fluid limit and vortex motion law of the nonlinear Schrödinger equation.Comm. Math. Phys.,200: 249–274.
Makhankov, V. G., Rybakov, Y. P. and Sanyuk, V. I., 1993. The skyrme model. Springer, Berlin, and Heidelberg.
Malozemoff, A. P. and Slonzewski, J. O., 1979. Magnetic Domain Walls in Bubble Materials. Academic Press, New York.
Neu, J., 1990. Vortices in the complex scalar fields.Phys. D.,43: 385–406.
O'Dell, T. H., 1981. Ferromagnetodynamics, the Dynamics of Magnetic Bubbles, Domain and Domain Walls. Wiley, New York.
Papanicolaou, N. and Tomaras, T. N., 1991. Dynamics of magnetic vortices.Nuclear Phys. B,360: 425–462.
Rajaraman, R., 1982. Solitons and Instantons. North-Holland, Amsterdam.
Shatah, J., 1988. Weak solutions and development of singularities of theSU(2)-ω-model.Comm. Pure and Appl. Math.,41: 459–469.
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Project supported partially by the NSF grant, USA and Chang-Jiang Professor Fund at Zhejiang University, China
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Fang-hua, L., Jalal, S. Soliton dynamics in planar ferromagnets and anti-ferromagnets. J. Zhejiang Univ. Sci. A 4, 503–510 (2003). https://doi.org/10.1631/jzus.2003.0503
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DOI: https://doi.org/10.1631/jzus.2003.0503