Fronts in dissipative Fermi-Pasta-Ulam-Tsingou chains
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909883713978368 |
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| author | Herrmann, Michael James, Guillaume Matthies, Karsten |
| author_facet | Herrmann, Michael James, Guillaume Matthies, Karsten |
| contents | In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly compressed (or stretched) states at $\pm \infty$ using an implicit function argument starting at a suitable continuum limit in the case of large damping. A detailed analysis allows us to show monotonicity of waves and to determine sharp exponential decay rates for a wide class of potentials including Hertzian potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fronts in dissipative Fermi-Pasta-Ulam-Tsingou chains Herrmann, Michael James, Guillaume Matthies, Karsten Analysis of PDEs Dynamical Systems In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly compressed (or stretched) states at $\pm \infty$ using an implicit function argument starting at a suitable continuum limit in the case of large damping. A detailed analysis allows us to show monotonicity of waves and to determine sharp exponential decay rates for a wide class of potentials including Hertzian potentials. |
| title | Fronts in dissipative Fermi-Pasta-Ulam-Tsingou chains |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2503.19518 |