Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy
arXiv:0711.1644 · doi:10.1111/j.1467-9590.2008.00405.x
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.
arXiv comment49 pages
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Cited by in corpus (9)
- Algebro-Geometric Finite-Gap Solutions of the Ablowitz-Ladik Hierarchy
- Discrete integrable systems and random Lax matrices
- Symmetries for the Ablowitz-Ladik hierarchy: I. Four-potential case
- The semi-discrete AKNS system: Conservation laws, reductions and continuum limits
- Minimal Rank Decoupling of Full-Lattice CMV Operators with Scalar- and Matrix-Valued Verblunsky Coefficients
- The Ablowitz-Ladik Hierarchy Revisited
- A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
- On the spatial asymptotics of solutions of the Ablowitz-Ladik hierarchy
- On universality of critical behaviour in Hamiltonian PDEs