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| We study the dynamics of a class of non-autonomous Hamiltonian systems consisting of a periodic sequence of linear and nonlinear autonomous parts and focus on their control capabilities in terms of altering the global phase space structure of the motion. One degree of freedom systems are studied which model solitary wave formation in transversely inhomogeneous configurations such as planar nonlinear optical structures or Bose-Einstein condensates. When one of the two alternating parts is linear, the solutions of the system are closely related to those of the nonlinear autonomous part. When the nonlinear parts have alternating signs, all types of solitary waves can be formed, including bright, dark, anti-dark and kink solitons as well as bound states. We also study multi-degree of freedom systems such as a nonautonomous Toda lattice with pulsating coupling, whose breathers are directly related to the solitons of the corresponding autonomous Toda lattice, while a ``ratchet'' effect provides a mechanism for their velocity and collision control. Finally, we consider a Klein-Gordon particle chain with long range interactions and switch on and off the inter-particle harmonic coupling to examine oits effect on breather formation, stability and the dynamics of wave packet diffusion. |
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