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.

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.