## Some exact solutions to multidimensional Landau-Lifshitz equation with uprush external field and anisotropy field.(English)Zbl 1172.35348

Summary: We give a method that can construct some exact solutions to a multidimensional Landau-Lifshitz equation with uprush external field and anisotropy field.

### MSC:

 35C05 Solutions to PDEs in closed form 35A25 Other special methods applied to PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 82D45 Statistical mechanics of ferroelectrics

exact transform
Full Text:

### References:

 [1] Landau, L.D.; Lifshitz, E.M., On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, Z. sowjetunion, 8, (1935), Reproduced in Collected Papers of L.D. Landau, Pergamon, New York, 1965, pp. 101-114 · Zbl 0012.28501 [2] Nakamura, K.; Sasada, T., Soliton and wave trains in ferromagnets, Phys. lett. A, 48, 321-322, (1974) [3] Tjon, J.; Wright, J., Soliton in the hesenberg chain, Phys. rev. B, 15, 3470-3476, (1977) [4] Lakshmanan, M.; Ruijgrok, T.w.; Thompson, C.J., On the dynamics of a continuous spin systems, Physica A, 84, 577-590, (1976) [5] Eleonskiĭ, V.M.; Kirova, N.N.; Petrov, V.M., General type of solutions of the landau – lifshitz equations, Sov. phys. JETP, 41, 5, 966-970, (1975) [6] Yue, Hong; Chen, Xiang-Jun; Huang, Nian-Ning, An inverse scattering transform for the landau – lifshitz equation for a spin chain with an easy plane, J. phys. A, 31, 10, 2491-2501, (1998) · Zbl 0920.35148 [7] Sadakane, T., Soliton solutions of $$X X Z$$ lattice landau – lifshitz equation, J. math. phys., 42, 11, 5457-5471, (2001) · Zbl 1063.82006 [8] Gustafson, S.; Shatah, J., The stability of localized solutions of landau – lifshitz equations, Commun. pure appl. math., LV, 5, 1136-1159, (2002) · Zbl 1028.35059 [9] Chapter four in Yang Ganshan’s Doctor Thesis, Beijing [10] Guo, Boling; Han, Yongqian; Yang, Ganshan, Blow up problem for landau – lifshitz equations in two dimensions, Commun. nonlinear sci. numer. simul., 5, 1, 43-44, (2000) · Zbl 0952.35143 [11] Guo, Boling; Han, Yongqian; Yang, Ganshan, Exact blow-up solutions for multidimensional landau – lifshitz equations, Adv. math. (China), 30, 1, 91-93, (2001) · Zbl 0999.35094 [12] Guo, Boling; Yang, Ganshan, Some exact nontrivial global solutions with values in unit sphere for two-dimensional landau – lifshitz equations, J. math. phys., 42, 5223-5227, (2001) · Zbl 1063.35047 [13] Yang, Ganshan; Chang, Qianshun, Limit behavior of solution for multidimensional landau – lifshitz equations with external magnetic field, Phys. lett. A, 318, 3, 270-280, (2003) · Zbl 1045.35073 [14] Svendsen, Michael; Fogedby, Hans C., Phase shift analysis of the landau – lifshitz equation, J. phys. A, 26, 7, 1717-1730, (1993) · Zbl 0774.35068 [15] Sen, Shibani; Roy Chowdhury, A., On the invariance properties and conservation laws for landau – lifshitz equation in three dimensions with tijon-wright ansatz, J. math. phys., 32, 9, 2343-2346, (1991) · Zbl 0737.35081 [16] Roelofs, G.H.M.; Martini, R., Prolongation structure of the landau – lifshitz equation, J. math. phys., 34, 6, 2394-2399, (1993) · Zbl 0776.35060 [17] Skrypnyk, T., ‘doubled’ generalized landau – lifshitz hierarchies and special quasigraded Lie algebras, J. phys. A, 37, 31, 7755-7768, (2004) · Zbl 1063.22025 [18] Kosevich, A.M.; Ivanov, B.A.; Kovalev, A.S., Magnetic solitons, Phys. rep., 194, 3-4, 117-238, (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.