We introduce two novel methods for studying periodic solutions of the FPU beta-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.
Arioli, G., Koch, H., Terracini, S. (2005). Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 255(1), 1-19 [10.1007/s00220-004-1251-z].
Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model
TERRACINI, SUSANNA
2005
Abstract
We introduce two novel methods for studying periodic solutions of the FPU beta-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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