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Complete integrability and multisoliton solutions are discussed for a multicomponent Ablowitz-Ladik system with branched dispersion relation. It is also shown that starting from a diagonal (in two-dimensions) completely integrable Ablowitz-Ladik equation, one can obtain all the results using a periodic reduction.
We construct a local tri-Hamiltonian structure of the Ablowitz-Ladik hierarchy, and compute the central invariants of the associated bihamiltonian structures. We show that the central invariants of one of the bihamiltonian structures are equal to 1/2
We construct the Baxters operator and the corresponding Baxters equation for a quantum version of the Ablowitz Ladik model. The result is achieved by looking at the quantum analogue of the classical Backlund transformations. For comparison we find th
The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised discrete P
It is shown that, three different Lax operators in the Dym hierarchy, produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component KdV system. The first equation gives us know
In their reply arXiv:1408.2230, the authors corrected some inappropriate sentences and clarified misleading descriptions in their original manuscript arXiv:1407.5194v1.