Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to $u_{tt}-u_{xx}\pm u^{3}=0$

Filip Ficek; Maciej Maliborski

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Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to u_(tt)-u_(xx)pm u³=0

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arxiv 2408.05158 v2 pith:H4VXZADY submitted 2024-08-09 math.AP math-phmath.MP

Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to u_(tt)-u_(xx)pm u³=0

Filip Ficek , Maciej Maliborski This is my paper

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We propose a systematic approach to analysing the complex structure of time-periodic solutions to the cubic wave equation on an interval with Dirichlet boundary conditions first reported in arXiv:2407.16507. The analysis we present is based on a detailed study of sparse mode interactions suggested by the previous numerical work. Our results complement prior rigorous existence proofs and suggest that solutions exist for any frequency, however, they may be arbitrarily large.

Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to u_(tt)-u_(xx)pm u³=0

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