Exact dynamics for fully connected nonlinear networks
arXiv:1101.4721 · doi:10.1016/j.physleta.2011.01.049
Abstract
We investigate the dynamics of the discrete nonlinear Schrödinger equation in fully connected networks. For a localized initial condition the exact solution shows the existence of two dynamical transitions as a function of the nonlinearity parameter, a hyperbolic and a trigonometric one. In the latter the network behaves exactly as the corresponding linear one but with a renormalized frequency.
6 pages, 2 figures