Solitons and wave trains in ferromagnets

The Difference Format of Landau-Lifshitz Equation in Two-dimensional Case

“…In 1974, Nakamura and Sasada research the following equation in the case of one-dimensional motion in [15]: .Therefore, we can conclude that the method is stable. Figure 3 We can conclude that the graphs will be blowup when time 1 2 t , thus we will improve and change designs of the numerical differential scheme.…”

Explicit piecewise smooth solutions of Landau-Lifshitz equation with discontinuous external field

“…On the case of one-dimensional motion, in 1974, Nakamura and Sasada studied (1.1) under non-vanishing external magnetic field (this is λ(t) ≡ 1, H = (0, 0, h 3 ) = 0) in [7]. They found the following solitary wave ⎧ ⎪ ⎨ ⎪ ⎩ u 1 = sin θ cos φ, u 2 = sin θ sin φ, u 3 = cos θ. where…”

Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

“…However, when an anisotropic parameter approaches vanished this solution does not tend to the well-known solution of an isotropic chain. Using the variation method, Nakumura et al [10] obtained a solution. If this solution is directly substituted to the equation of motion, it does not satisfy the equation.…”

“…Its study is of considerable interest, especially from the points of view of both soliton theory and condensed matter physics. In particular, its continuum limit is governed by the wellknown Landau-Lifschitz equation, and it displays fascinating geometrical aspects: an isotropic [8,9] and an uniaxial anisotropic [10][11][12] system is geometrically equivalent and gauge equivalent to a nonlinear Schrodinger equation. These as well as the biaxial anisotropic [13][14][15][16] systems are completely integrable.…”