Abstract
Let Ω be a domain in m-dimensional Enclidean space R m. The n-dimensional classical system for the isotropic Heisenberg chain with spin density Z i (x, t) (i = 1, 2, 3) is described by the Hamiltonian density
where α2 is the exchange constant, \( \vec{Z} \) is the spin veetor and H 0 an external magnetie field. The spin equation of motion with Gilbert damping term (without the external magnetic field) has the form
where “ ×” denotes the vector cross product in \( {{R}^{3}},\vec{Z} = ({{Z}_{1}},{{Z}_{2}},{{Z}_{3}}):\Omega \times [0,T] \to {{R}^{3}} \) is the spin vector and α1≥0 is a Gilbert damping constant (see [1]). The system (0.1) is implied by the conservation of energy and magnitude of \( \vec{Z} \), and is aversion which gives rise to a continuum spin wave theory.
1991 Mathematics Subject Classification: 35Q
Supported by the National Natural Science Fund of China
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© 1994 Springer Science+Business Media Dordrecht
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Zhou, Y., Guo, B. (1994). Nonlinear Partial Differential Equations in Physics and Mechanics. In: Gu, C., Ding, X., Yang, CC. (eds) Partial Differential Equations in China. Mathematics and Its Applications, vol 288. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1198-0_10
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