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

Fritz Gesztesy, Helge Holden, Johanna Michor, and Gerald Teschl

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.

MSC2000: Primary 37K10, 37K20, 47B36; Secondary 35Q58, 37K60.
Keywords: Ablowitz-Ladik hierarchy, Hamiltonian formalism, conservation laws.

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