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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.06932 |
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| _version_ | 1866918062706393088 |
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| author | Hofstrand, Andrew |
| author_facet | Hofstrand, Andrew |
| contents | The unique geometry of the two-dimensional tripartite Kagome lattice is responsible for shaping diverse families of spatially localized and time-periodic nonlinear modes known as discrete breathers. We state conditions for the existence of breathers and compute their spatiotemporal profiles near the edges of the linear phonon spectrum. Our findings include the existence of strongly nonlinear and dynamically stable breathers inside the band gap on the infinite lattice, asymptotic expressions for breather energy thresholds in the weakly nonlinear regime, and explicit breather solutions that remain compactly supported on the lattice and undergo stability transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Families of Discrete Breathers on a Nonlinear Kagome Lattice Hofstrand, Andrew Pattern Formation and Solitons The unique geometry of the two-dimensional tripartite Kagome lattice is responsible for shaping diverse families of spatially localized and time-periodic nonlinear modes known as discrete breathers. We state conditions for the existence of breathers and compute their spatiotemporal profiles near the edges of the linear phonon spectrum. Our findings include the existence of strongly nonlinear and dynamically stable breathers inside the band gap on the infinite lattice, asymptotic expressions for breather energy thresholds in the weakly nonlinear regime, and explicit breather solutions that remain compactly supported on the lattice and undergo stability transitions. |
| title | Families of Discrete Breathers on a Nonlinear Kagome Lattice |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2412.06932 |