Stud. Appl. Math. 120-4, 361-423 (2008).
 [DOI: 10.1111/j.1467-9590.2008.00405.x]

Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy

F. Gesztesy, H. Holden, J. Michor, and G. Teschl

Keywords: Ablowitz-Ladik hierarchy, Hamiltonian formalism, conservation laws.

Abstract: We derive a systematic and recursive approach to local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik (AL) hierarchy. Our methods rely on a recursive approach to the AL hierarchy using Laurent polynomials and on asymptotic expansions of the Green's function of the AL Lax operator, a five-diagonal finite difference operator.

MSC: Primary 37K10, 37K20, 47B36; Secondary 35Q58, 37K60.

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ESI Preprint 1977
arXiv:0711.1644

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