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• W3105490889 abstract "We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski and Maliborski on the existence of time periodic solutions to the spherically symmetric Einstein–Klein–Gordon system, we study perturbations around the zero solution as a formal series expansion and assume that the perturbations bifurcate from one mode. In the center of this work stands a rigorous proof on how one can choose the initial data to cancel out all secular terms in the resonant system. Interestingly, our analysis reveals that the only possible choice for the existence of time periodic solutions bifurcating from the first mode is when the error terms in the expansion are all proportional to this dominant one mode. Finally, we use techniques from ordinary differential equations and establish the existence of time periodic solutions for the initial data proportional to the first mode of the linearized operator." @default.
• W3105490889 created "2020-11-23" @default.
• W3105490889 creator A5050763931 @default.
• W3105490889 date "2020-11-01" @default.
• W3105490889 modified "2023-09-26" @default.
• W3105490889 title "On time periodic solutions to the conformal cubic wave equation on the Einstein cylinder" @default.
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• W3105490889 doi "https://doi.org/10.1063/5.0026015" @default.
• W3105490889 hasPublicationYear "2020" @default.
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