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Dynamics of Self-Trapping in the Discrete Nonlinear Schrödinger Equation
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We study dynamical aspects of the discrete nonlinear Schrödinger equation (DNLS) for chains of different sizes with periodic and open boundary conditions. We focus on the occurrence of a self-trapping transition in the different geometries. The initial condition used is that which places the particle (or power) on one lattice site (or nonlinear waveguide) and the quantity studied is the time-averaged probability for the particle to remain in that site. We show that the self-trapping transition in long chains occurs for parameter values not very different from that for very small clusters.
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