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
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.