Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

• Published in: Annals of PDE Vol. 9; no. 1; p. 2
• Main Authors: Ishizuka, Kenjiro, Nakanishi, Kenji
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2023; Springer Nature B.V
• Subjects: Damping; Decomposition; Eigenvalues; Energy; Euclidean geometry; Ground state; Klein-Gordon equation; Manifolds (mathematics); Mathematical Methods in Physics; Nonlinearity; Partial Differential Equations; Physics; Physics and Astronomy; Solitary waves; Solitons; Secondary 37L25; 35B30; 35B40; Nonlinear Klein-Gordon equation; Invariant manifolds; Blow-up; Primary 35L71

Global behavior of solutions is studied for the nonlinear Klein-Gordon equation with a focusing power nonlinearity and a damping term in the energy space on the Euclidean space. We give a complete classification of solutions into 5 types of global behavior for all initial data in a small neighborhoo...