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- Title
Long-time Asymptotics of the One-dimensional Damped Nonlinear Klein–Gordon Equation.
- Authors
Côte, Raphaël; Martel, Yvan; Yuan, Xu
- Abstract
For the one-dimensional nonlinear damped Klein–Gordon equation ∂ t 2 u + 2 α ∂ t u - ∂ x 2 u + u - | u | p - 1 u = 0 on R × R , with α > 0 and p > 2 , we prove that any global finite energy solution either converges to 0 or behaves asymptotically as t → ∞ as the sum of K ≥ 1 decoupled solitary waves. In the multi-soliton case K ≥ 2 , the solitary waves have alternate signs and their distances are of order log t .
- Subjects
KLEIN-Gordon equation; NONLINEAR equations; SINE-Gordon equation; MATHEMATICAL decoupling; GLOBAL analysis (Mathematics)
- Publication
Archive for Rational Mechanics & Analysis, 2021, Vol 239, Issue 3, p1837
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-020-01605-4