Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
In: Journal of Mathematical Physics ; volume 52, issue 10 ; ISSN 0022-2488 1089-7658, 2011
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Zugriff:
We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation utt − uxx + u − |u|2αu = 0 on the line. Using mixed numerical and analytical methods we find that solutions starting from even initial data, fine-tuned to the threshold, are trapped by the static solution S for intermediate times. The details of trapping are shown to depend on the power α, namely, we observe fast convergence to S for α > 1, slow convergence for α = 1, and very slow (if any) convergence for 0 < α < 1. Our findings are complementary with respect to the recent rigorous analysis of the same problem (for α > 2) by Krieger, Nakanishi, and Schlag [“Global dynamics above from the ground state energy for the one-dimensional NLKG equation,” preprint arXiv:1011.1776 [math.AP]].
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Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
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Autor/in / Beteiligte Person: | Bizoń, Piotr ; Chmaj, Tadeusz ; Szpak, Nikodem |
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Zeitschrift: | Journal of Mathematical Physics ; volume 52, issue 10 ; ISSN 0022-2488 1089-7658, 2011 |
Veröffentlichung: | AIP Publishing, 2011 |
Medientyp: | academicJournal |
DOI: | 10.1063/1.3645363 |
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