Exact dynamics for fully connected nonlinear networks

Details Exact dynamics for fully connected nonlinear networks Exact dynamics for fully connected nonlinear networks

2011-01-25

arxiv.org/abs/1101.4721v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, 2 figures

Scientific paper

We investigate the dynamics of the discrete nonlinear Schr\"{o}dinger 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.

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