Some periodic and blow-up solutions for Landau-Lifshitz equation. (English) Zbl 1274.82095
Summary: In this paper, we construct the exact solution of two- or three-dimensional spacetime Landau-Lifshitz equation raised in the ferromagnetic materials. Under suitable transformations, some exact solutions are obtained in the radially symmetric coordinates and nonsymmetric coordinates. The type of solutions cover the finite time blow-up solution, vortex solution and periodic solution. In the end, we sketch some solutions and their spatial curvatures.
MSC:
| 82D40 | Statistical mechanics of magnetic materials |
| 35B44 | Blow-up in context of PDEs |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T25 | Quantum field theory on lattices |
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