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Nonlinear spin excitations in a classical Heisenberg anisotropic helimagnet. (English) Zbl 1186.82099

Summary: The nonlinear spin excitations in an anisotropic helimagnet in the presence of a constant magnetic field are investigated in the classical continuum limit. The helical character is introduced into the model, in analogy with the twist in a cholesteric liquid crystal. After deriving a class of spin wave solutions for the stereographic representation of the Landau-Lifshitz equation, in-plane stationary spin configurations are obtained and their stability is analysed. When the external magnetic field is along the anisotropic axis, modulational instability is observed in the spin lattice, and when the external magnetic field is normal to the anisotropic axis, the spin configurations are unstable. The perturbed spin components show fluctuations in the tail region, while the velocity and amplitude of the soliton remain unaltered.

MSC:

82D40 Statistical mechanics of magnetic materials
35Q60 PDEs in connection with optics and electromagnetic theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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