Theory and Modern Applications
Table 4 Variable separation solution of the equivalent LLG equation without damping (see equation (60)). F satisfies (71); \(F_{2}\) is the solution of (99)
Solutions I–II | Decay rate |
|---|---|
Solution I: \(\mathrm{e}^{F}\exp [i ( C_{{1}}+ C_{{2}}\int {r}^{-n+1} ( {\mathrm{e}^{2 F}}+1 )^{2} {\mathrm{e}^{-2 F}} \,\mathrm{d}r + C_{5}t ) ]\) | \(\frac{1}{r^{n-1}}\), (n ≥ 2); |
O(1), (n = 1) | |
Solution II: \(\mathrm{e}^{F_{2}}\exp [i ( C_{{1}}+ C_{{2}}\int ( {\mathrm{e}^{2 F_{2}}}+1 )^{2} {\mathrm{e}^{-2 F_{2}}} \,\mathrm{d}\overline{r} + C_{5}t ) ] \) | O(1) |