Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy

Details Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy

2007-11-11

arxiv.org/abs/0711.1644v1

Stud. Appl. Math. 120-4, 361-423 (2008)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

49 pages

Scientific paper

10.1111/j.1467-9590.2008.00405.x

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.

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