Asymptotic stability near the soliton for quartic Klein-Gordon in 1D
| Autor: | Kairzhan, Adilbek, Pusateri, Fabio |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Pure Appl. Analysis 5 (2023) 795-832 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/paa.2023.5.795 |
| Popis: | We consider the nonlinear focusing Klein-Gordon equation in $1 + 1$ dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof of optimal decay, and local decay, for even perturbations of the static soliton originating from well-prepared initial data belonging to a subset of the stable manifold constructed in Bates-Jones (Dynamics reported, 1989) and Kowalczyk-Martel-Mu\~noz (J. Eur. Math. Soc., 2021). Our results complement those of Kowalczyk-Martel-Mu\~noz (J. Eur. Math. Soc., 2021) and confirm numerical results of Bizon-Chmaj-Szpak (J. Math. Phys., 2011) when considering nonlinearities $u^p$ with $p \geq 4$. In particular, we provide new information both local and global in space about asymptotically stable perturbations of the soliton under localization assumptions on the data. Comment: 35 pages, no figures |
| Databáze: | arXiv |
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