Abstract
We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference. Differing from the works appearing in the above two references, a new discrete integrable system is obtained by the generalized Ablowitz-Ladik hierarchy; the Darboux transformation of this new discrete integrable system is established further. As applications of this Darboux transformation, different kinds of exact solutions of this new system are explicitly given. Investigatingthe properties of these exact solutions, we find that these exact solutions are not pure soliton solutions, but their dynamic characteristics are very interesting.
Highlights
It is well known that the nonlinear integrable lattice systems have been intensively investigated in many scientific fields such as physics, chemistry, and biology
Among the multitudinous new integrable hierarchies, we will discuss the so-called new discrete lattice system which is given by 21, equation 2.12 qn,t qn[2] rn 1 − qn−1, rn,t −rn2qn−1 rn 1, 1.1 which is derived by Qin
We show that the discrete system 1.1 which is given by Qin in can be reduced to the old integrable lattice system which is given by Merola et al
Summary
It is well known that the nonlinear integrable lattice systems have been intensively investigated in many scientific fields such as physics, chemistry, and biology. Some new lattice hierarchies and their integrability, Darboux transformation, conversation law, exact solution, and dynamic characteristics have been holding more and more attention. The results investigated by Qin in are different from those given in ; these two systems are equivalent under the above coordinate transformations, noting that the coordinate scales of these two systems are different, and both work are interesting and very useful.
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