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.