Stability of bound states of Hamiltonian PDEs in the degenerate cases
  We consider a Hamiltonian systems which is invariant under a one-parameter unitary group. We give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schr\"odinger equation. 
Masaya Maeda
math.AP