Functional representation of the Ablowitz-Ladik hierarchy. II
arXiv:solv-int/9812020 · doi:10.2991/jnmp.2002.9.2.3
Abstract
In this paper I continue studies of the functional representation of the Ablowitz-Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition I rederive the functional equations for the tau-functions of the ALH and obtain some new equations which provide more straightforward description of the ALH and which were absent in the previous paper. These results are used to establish relations between the ALH and the discrete-time nonlinear Schrodinger equations, to deduce the superposition formulae (Fay's identities) for the tau-functions of the hierarchy and to obtain some new results related to the Lax representation of the ALH and its conservation laws. Using the previously found connections between the ALH and other integrable systems I derive functional equations which are equivalent to the AKNS, derivative nonlinear Schrodinger and Davey-Stewartson hierarchies.
arxiv version is already official
References in corpus (6)
- Solution of the dispersionless Hirota equations
- Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
- Functional representation of the Ablowitz-Ladik hierarchy
- A note on the integrable discretization of the nonlinear Schrödinger equation
- Finite genus solutions for the Ablowitz-Ladik hierarchy
- On an integrable discretization of the modified Korteweg-de Vries equation
Cited by in corpus (23)
- Lattice representation and dark solitons of the Fokas-Lenells equation
- Functional representations of integrable hierarchies
- Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik Hierarchy
- From AKNS to derivative NLS hierarchies via deformations of associative products
- Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy
- Algebro-Geometric Finite-Gap Solutions of the Ablowitz-Ladik Hierarchy
- Nonassociativity and Integrable Hierarchies
- Functional representation of the negative AKNS hierarchy
- Conservation laws for the nonlinear Schrodinger equation in Miwa variables
- On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system
- Integrable semi-discretization of the massive Thirring system in laboratory coordinates
- Soliton Fay identities. II. Bright soliton case
- Solutions of matrix NLS systems and their discretisations: A unified treatment
- On a new integrable discretization of the derivative nonlinear Schrödinger (Chen-Lee-Liu) equation
- Explicit solutions for a (2+1)-dimensional Toda-like chain
- Bäcklund transformations between the AKNS and DNLS hierarchies
- Toda-Heisenberg chain: interacting sigma-fields in two dimensions
- Explicit solutions for a nonlinear model on the honeycomb and triangular lattices
- Solitons of a vector model on the honeycomb lattice
- Functional representation of the negative DNLS hierarchy
- The Ablowitz-Ladik Hierarchy Revisited
- Two-Dimensional Toda-Heisenberg Lattice
- Explicit Solutions for a Nonlinear Vector Model on the Triangular Lattice