On dynamics of the discrete NLS equation
Milutin S. Stepic, Lj. R. Hadzievski, M. M. Skoric
Vinca Institute of Nuclear Sciences, P. O. Box 522,
Belgrade University, Yugoslavia.
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.