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On dynamics of the discrete NLS equation
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**Milutin S. Stepic, Lj. R. Hadzievski, M. M. Skoric
**

*Vinca Institute of Nuclear Sciences, P. O. Box 522,
Belgrade University, Yugoslavia.
*

**Abstract: **
Recently so called continious-discrete nonlinear systems, where both
the discretness and temporal dispersion are taken into account, have
attracted a lot of attention in optics and plasma physics.
We investigate soliton-like dynamics in the discrete nonlinear
Schrödinger equation (DNLSE) describing the generic 3-element discrete
nonlinear system with a dispersion. The DNLSE (1+2) is solved on the 3*K
discrete lattice, where K is the variable number introduced through the
discretized dispersion term. In quasi linear and strongly nonlinear
regimes the evolution shows robustness with respect to the K variation.
The intermediate regime often exibiting chaos, appears highly sensitive
to the number of discrete points, making an exact solving of the DNLSE
(1+2) a dubious task.