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Breather solutions of the cubic Klein–Gordon equation

Scheider, Dominic

Abstract:
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein–Gordon equation ${\partial }_{t}^{2}U-{\Delta}U+{m}^{2}U={\Gamma}\left(x\right){U}^{3}\;\text{on}\;\mathbb{R}{\times}{\mathbb{R}}^{3},$ which are weakly localized in space. Various families of such 'breather' solutions are shown to bifurcate from any given nontrivial stationary solution. The construction of weakly localized breathers in three space dimensions is, to the author's knowledge, a new concept and based on the reformulation of the cubic Klein–Gordon equation as a system of coupled nonlinear Helmholtz equations involving suitable conditions on the far field behavior.

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Verlagsausgabe §
DOI: 10.5445/IR/1000128382
Veröffentlicht am 12.01.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 12.2020
Sprache Englisch
Identifikator ISSN: 0951-7715, 1361-6544
KITopen-ID: 1000128382
Erschienen in Nonlinearity
Verlag IOP Publishing
Band 33
Heft 12
Seiten 7140–7166
Vorab online veröffentlicht am 11.11.2020
Nachgewiesen in Scopus
Web of Science
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