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Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
Late-time Kerr tails: generic and non-generic initial data sets,
generic non-generic superposition
2010/3/17
Three interrelated questions concerning Kerr spacetime late-time tails are considered, specifically the evolutions of generic and non-generic initial data sets, the excitation of "up" modes, and the r...
Analysis of Effectiveness of Lyapunov Control for Non-generic Quantum States
Analysis Lyapunov Control Non-generic Quantum States
2010/4/12
A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show ...