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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2602.07655 |
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| _version_ | 1866908819634782208 |
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| author | Hofstrand, Andrew |
| author_facet | Hofstrand, Andrew |
| contents | We study the dynamics of discrete breathers -- spatially localized and time-periodic solutions -- inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands cross linearly in one direction and quadratically in the orthogonal direction. By studying breather dynamics in two opposing asymptotic regimes, near the continuum and anti-continuum limits, we capture the features of hybrid coherent structures on the lattice that are highly discrete at the breather's central peak and have tails well approximated by exact separable solutions to an effective long-wave PDE theory at spatial infinity. We find that breathers are dynamically stable over a wide range of parameters and locate an instability transition. Finally, we analyze the Floquet stability of spatially extended nonlinear plane waves bifurcating from the zero solution at the edges of the gap and how they shape breather profiles inside the gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07655 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete Breathers in a Honeycomb Lattice Near a Semi-Dirac Point Hofstrand, Andrew Pattern Formation and Solitons We study the dynamics of discrete breathers -- spatially localized and time-periodic solutions -- inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands cross linearly in one direction and quadratically in the orthogonal direction. By studying breather dynamics in two opposing asymptotic regimes, near the continuum and anti-continuum limits, we capture the features of hybrid coherent structures on the lattice that are highly discrete at the breather's central peak and have tails well approximated by exact separable solutions to an effective long-wave PDE theory at spatial infinity. We find that breathers are dynamically stable over a wide range of parameters and locate an instability transition. Finally, we analyze the Floquet stability of spatially extended nonlinear plane waves bifurcating from the zero solution at the edges of the gap and how they shape breather profiles inside the gap. |
| title | Discrete Breathers in a Honeycomb Lattice Near a Semi-Dirac Point |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2602.07655 |