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タイトル: | Invariant Manifolds Around Soliton Manifolds for the Nonlinear Klein–Gordon Equation |
著者: | Nakanishi, K. https://orcid.org/0000-0002-8988-1726 (unconfirmed) Schlag, W. |
著者名の別形: | 中西, 賢次 |
キーワード: | nonlinear wave equation nonlinear Klein–Gordon equation stationary solution soliton stable manifold center-stable manifold |
発行日: | 2012 |
出版者: | Society for Industrial and Applied Mathematics |
誌名: | SIAM Journal on Mathematical Analysis |
巻: | 44 |
号: | 2 |
開始ページ: | 1175 |
終了ページ: | 1210 |
抄録: | 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. |
著作権等: | © 2012 Society for Industrial and Applied Mathematics |
URI: | http://hdl.handle.net/2433/158309 |
DOI(出版社版): | 10.1137/11082720X |
出現コレクション: | 学術雑誌掲載論文等 |
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