Invariant Manifolds Around Soliton Manifolds for the Nonlinear Klein–Gordon Equation

DOI10.1137/11082720XzbMath1261.35037arXiv1102.5583MaRDI QIDQ2904742

Kenji Nakanishi, Wilhelm Schlag

Publication date: 23 August 2012

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5583

zbMATH Keywords

nonlinear wave equationstable manifoldcenter-stable manifoldfamily of solitary wavesfocusing energy subcritical nonlinearitygraph transform method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

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Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space ⋮ Invariant manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space ⋮ Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation ⋮ Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations ⋮ Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes ⋮ Center-stable manifold of the ground state in the energy space for the critical wave equation ⋮ Dynamics near the solitary waves of the supercritical gKDV equations ⋮ Center stable manifolds around line solitary waves of the Zakharov-Kuznetsov equation with critical speed ⋮ Description and classification of \(2\)-solitary waves for nonlinear damped Klein-Gordon equations ⋮ Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

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