Invariant Manifolds and Dispersive Hamiltonian Evolution Equations

@inproceedings{Nakanishi2011InvariantMA,
  title={Invariant Manifolds and Dispersive Hamiltonian Evolution Equations},
  author={Kenji Nakanishi and Wilhelm Schlag},
  year={2011}
}
By means of certain dispersive PDEs (such as the nonlinear Klein-Gordon equation) we will exhibit a new family of phenomena related to the ground state solitons. These solitons are (exponentially) unstable, and one can construct stable, unstable, and center(-stable) manifolds associated with these ground states in the sense of hyperbolic dynamics. In terms of these invariant manifolds one can completely characterize the global dynamics of solutions whose energy exceeds that of the ground states… 

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