### Abstract

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 language | Undefined |
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Pages (from-to) | 2394-2399 |

Number of pages | 6 |

Journal | Journal of mathematical physics |

Volume | 34 |

DOIs | |

Publication status | Published - 1993 |

### Keywords

- METIS-140363
- IR-102313

## Cite this

Roelofs, G. H. M., Roelofs, M., & Martini, R. (1993). Prolongation structure of the Landau-Lifshitz equation.

*Journal of mathematical physics*,*34*, 2394-2399. https://doi.org/10.1063/1.530124