In many physical systems one can observe fast transitions between resonant states, i.e., states where some of the phase variables become commensurate. Examples include the phenomenon of ultrafast energy transfer in molecular dynamics, and the numerically observed jumping behavior of the perturbed nonlinear Schröodinger equation. In this talk I describe a global perturbation method to construct solutions that connect slow trajectories through fast, intermediate jumps. As applications, I discuss single and coupled NLS equations.

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