Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
34 (1993), S. 2394-2399
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The prolongation method of Wahlquist and Estabrook is applied to the Landau–Lifshitz equation. The resulting prolongation algebra is shown to be isomorphic to a subalgebra of the tensor product of the Lie algebra so(3) with the elliptic curve vα2−vβ2=jβ−jα (α,β=1,2,3), which is essentially a subalgebra of the Lie algebra applied by Date et al. in a different context. Taking a matrix representation of so(3) gives rise to a Lax pair of the Landau–Lifshitz equation in agreement with the results found by Sklyanin. A system of related equations is deduced which can be used for the computation of auto-Bäcklund transformations of the Landau–Lifshitz equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530124
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