Scattering of coupled particles on a potential well

This paper investigates the dynamics of scattering of a 2DOF system of coupled particles on a potential well. In the considered one-dimensional setting, the system can either pass through the well or rebound. If dissipative effects are included, another possible outcome is the system's trapping in the well. The scattering outcomes are intrinsically related to the energy transfer mechanisms between the coupled system and the well. For some initial conditions, one observes an extremely sensitive (chaotic-like) dependence of the scattering outcome. Relatively large initial velocities of the system or a relatively small free length of the internal coupling allow for an asymptotic approach and analytical prediction of the scattering outcomes and parameters. In particular, it is possible to predict the residual amplitudes of the oscillations of the coupled system and the transition to sensitive (chaotic-like) dynamics. The developed approaches and observed scattering patterns seem generic and applicable to a wide variety of similar models.