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Some Breathers and Multi-breathers for FPU-Type Chains

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Abstract

We consider several breather solutions for FPU-type chains that have been found numerically. Using computer-assisted techniques, we prove that there exist true solutions nearby, and in some cases, we determine whether or not the solution is spectrally stable. Symmetry properties are considered as well. In addition, we construct solutions that are close to (possibly infinite) sums of breather solutions.

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Authors and Affiliations

  1. Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Gianni Arioli

  2. Department of Mathematics, The University of Texas at Austin, Austin, TX, 78712, USA

    Hans Koch

Authors
  1. Gianni Arioli
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  2. Hans Koch
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Correspondence to Gianni Arioli.

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Communicated by C. Liverani

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G. Arioli: Supported in part by the PRIN project “Equazioni alle derivate parziali e disuguaglianze analitico-geometriche associate”.

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Arioli, G., Koch, H. Some Breathers and Multi-breathers for FPU-Type Chains. Commun. Math. Phys. 372, 1117–1146 (2019). https://doi.org/10.1007/s00220-019-03417-4

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  • DOI: https://doi.org/10.1007/s00220-019-03417-4

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