𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On integrable discretization of the inhomogeneous Ablowitz–Ladik model

✍ Scribed by V.V. Konotop

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
79 KB
Volume
258
Category
Article
ISSN
0375-9601

No coin nor oath required. For personal study only.

✦ Synopsis

An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it is shown that the step of the discretization must be comensurable with the period of oscillations imposed by the inhomogeneous force. By proper choice of the step of the discretization the period of oscillations of a soliton in the discrete model can be made equal to an integer number of periods of oscillations in the underline continuous-time lattice.

📜 SIMILAR VOLUMES

On an integrable discretization of the R
On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift
✍ Y. Nakamura; K. Kajiwara; H. Shiotani 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 695 KB

An integrable discretization of the Rayleigh quotient gradient system is established. The solution of the discrete gradient system is described explicitly and converges exponentially to the same equilibrium point as that of the continuous gradient system for arbitrary large difference step size. It

On the Numerical Solution of the Sine–Go
On the Numerical Solution of the Sine–Gordon Equation: I. Integrable Discretizations and Homoclinic Manifolds
✍ M.J. Ablowitz; B.M. Herbst; Constance Schober 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 614 KB

completely integrable through the inverse scattering transform (see, for example, [1,11]) this allows us to study the In this, the first of two papers on the numerical solution of the sine-Gordon equation, we investigate the numerical behavior of a subsequent nonlinear evolution of the instabilities