Nonlocal symmetries and recursion operator of the Landau-Lifshitz equation

Abstract

The Lie algebra of symmetries of the Landau-Lifshitz equation (LL) is discussed. Point, higher-order, and nonlocal symmetries of the LL are computed. The recursion operator is constructed from a nonlocal symmetry, reflecting the bi-Hamiltonian structure of the LL. The same recursion operator of the LL has been derived by Barouch, Fokas, and Papageorgiou [J. Math. Phys. 29, 2628 ( 1988)], starting from the Lax pair. © 1991 American Institute of Physics.