We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and propose a systematic framework for their analysis. A Floquet stability study reveals that this class contains solutions that are linearly stable, suggesting that they may play a significant role in the nonlinear dynamics of the systems.
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Project title:
Hin und zurück: über (quasi-)periodische Lösungen in der AR: P 36455 (FWF - Österr. Wissenschaftsfonds)
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Project (external):
FWF FWF
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Project ID:
10.55776/Y963 10.55776/Z387
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Research Areas:
Mathematical and Algorithmic Foundations: 50% Modeling and Simulation: 50%
