Global dynamics above the ground state energy for the one-dimensional NLKG equation

摘要: In this paper we obtain a global characterization of the dynamics even solutions to one-dimensional nonlinear Klein–Gordon (NLKG) equation on line with focusing nonlinearity \({|u|^{p-1}u, p >5 }\) , provided their energy exceeds that ground state only sightly. The method is same as in three-dimensional case (Nakanishi and Schlag Global above for Klein-Gordon equation, preprint, 2010), major difference being construction center-stable manifold. difficulty there lies weak dispersive decay 1-dimensional NLKG. order address specific issue, establish local estimates perturbed linear similar those Mizumachi (J Math Kyoto Univ 48(3):471–497, 2008). essential ingredient latter class absence threshold resonance linearized operator.