Abstract
We introduce two novel methods for studying periodic solutions of the FPU β-model, both numerically and rigorously. One is a variational approach, based on the dual formulation of the problem, and the other involves computer-assisted proofs. These methods are used e.g. to construct a new type of solutions, whose energy is spread among several modes, associated with closely spaced resonances.
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Communicated by G. Gallavotti
This work was supported in part by MIUR project “Metodi variazionali ed Equazioni Differenziali Non Lineari”.
This work was supported in part by the National Science Foundation under Grant No. DMS-0088935.
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Arioli, G., Koch, H. & Terracini, S. Two Novel Methods and Multi-Mode Periodic Solutions for the Fermi-Pasta-Ulam Model. Commun. Math. Phys. 255, 1–19 (2005). https://doi.org/10.1007/s00220-004-1251-z
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DOI: https://doi.org/10.1007/s00220-004-1251-z