• Corpus ID: 247597052

Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry

@inproceedings{Li2022SolitonDF,
  title={Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry},
  author={Yongming Li and Jonas Luhrmann},
  year={2022}
}
We establish the conditional asymptotic stability in a local energy norm of the unstable soliton for the one-dimensional quadratic Klein-Gordon equation under even perturbations. A key feature of the problem is the positive gap eigenvalue exhibited by the linearized operator around the soliton. Our proof is based on several virial-type estimates, combining techniques from the series of works [23–26,28], and an explicitly verified Fermi Golden Rule. The approach hinges on the fact that even… 
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