On recursion operators for elliptic models

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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16 pages, no figures

Scientific paper

New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov and the Landau-Lifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple of operators related by an elliptic curve equation. A theoretical explanation of this fact for the Landau-Lifshitz equation is given in terms of multiplicators of the corresponding Lax structure.

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