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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
$$\partial_t^2U-\Delta U+m^2U = \Gamma(x)U^3\quad\text{on } \mathbb{R}\times\mathbb{R}^3,$$
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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Volltext §
DOI: 10.5445/IR/1000104906
Veröffentlicht am 14.01.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000104906
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2020/1
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Klein–Gordon equation, breather, bifurcation, Helmholtz equation
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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