Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908606675288064 |
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| author | Duong, M. H. Reynolds, M. J. |
| author_facet | Duong, M. H. Reynolds, M. J. |
| contents | The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane - a second-order nonlinear ODE related to the Klein-Gordon equation with quadratic nonlinearity. These admit the well-known $\mathrm{sech}^2$ solutions, which we employ as an ansätz following [Deng et.al., PRL, 2017]. The resulting analysis yields soliton amplitudes and velocities that agree closely with numerical simulations, achieving an improvement of exactly 1/9 relative to the benchmark reported by the Harvard group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials Duong, M. H. Reynolds, M. J. Pattern Formation and Solitons Mathematical Physics The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane - a second-order nonlinear ODE related to the Klein-Gordon equation with quadratic nonlinearity. These admit the well-known $\mathrm{sech}^2$ solutions, which we employ as an ansätz following [Deng et.al., PRL, 2017]. The resulting analysis yields soliton amplitudes and velocities that agree closely with numerical simulations, achieving an improvement of exactly 1/9 relative to the benchmark reported by the Harvard group. |
| title | Phase-Space Analysis of Elastic Vector Solitons in Flexible Mechanical Metamaterials |
| topic | Pattern Formation and Solitons Mathematical Physics |
| url | https://arxiv.org/abs/2510.19837 |