Prolongation structure of the Landau-Lifshitz equation

G.H.M. Roelofs, Marcel Roelofs, Ruud Martini

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    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 v α 2−v β 2=j β−j α (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.
    Original languageUndefined
    Pages (from-to)2394-2399
    Number of pages6
    JournalJournal of mathematical physics
    Publication statusPublished - 1993


    • METIS-140363
    • IR-102313

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