Abstract
Abstract : During the period of this grant the investigators addressed nonlinear resonance and interactions involving systems of nonlinear ordinary differential equations with slowly varying coefficients. More specifically, they investigated passage through resonance, sustained resonance as in roll resonance, particle accelerators or free electron lasers, global adiabatic invariants and weakly nonlinear wave interactions. Approaches used included matching asymptotic expansions, multiple scale expansions, higher order averaging, the Melnikov method and near identity canonical transformations to obtain global adiabatic invariants. (Author)
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