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arxiv: 1107.3629 · v1 · pith:QNZJPWKHnew · submitted 2011-07-19 · 🧮 math.AP

Stability of bound states of Hamiltonian PDEs in the degenerate cases

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keywords bounddegenerateequationhamiltoniannonlinearpowerstabilitystates
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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.

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