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Title: Invariant Manifolds Around Soliton Manifolds for the Nonlinear Klein–Gordon Equation
Authors: Nakanishi, K.  kyouindb  KAKEN_id  orcid (unconfirmed)
Schlag, W.
Author's alias: 中西, 賢次
Keywords: nonlinear wave equation
nonlinear Klein–Gordon equation
stationary solution
stable manifold
center-stable manifold
Issue Date: 2012
Publisher: Society for Industrial and Applied Mathematics
Journal title: SIAM Journal on Mathematical Analysis
Volume: 44
Issue: 2
Start page: 1175
End page: 1210
Abstract: We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein–Gordon equation with a focusing energy subcritical nonlinearity, associated with a family of solitary waves which is generated from any radial stationary solution by the action of all Lorentz transforms and spatial translations. The construction is based on the graph transform (or Hadamard) approach, which requires less spectral information on the linearized operator, and less decay of the nonlinearity, than the Lyapunov–Perron method employed previously in this context. The only assumption on the stationary solution is that the kernel of the linearized operator is spanned by its spatial derivatives, which is known to hold for the ground states. The main novelty of this paper is that the graph transform method is carried out in the presence of modulation parameters corresponding to the symmetries.
Rights: © 2012 Society for Industrial and Applied Mathematics
DOI(Published Version): 10.1137/11082720X
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