A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular $\beta$-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular $\beta$-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

中文翻译：

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三角形β-Fermi-Pasta-Ulam-Tsingou晶格中的离散呼吸

在三角形中搜索（准）离散呼吸器（DB）的实用方法 $\beta$提出了-FPUT晶格（在Fermi，Pasta，Ulam和Tsingou之后）。通过将定位函数叠加在频率高于晶格声子谱的离域非线性振动模（DNVM）上来获得DB。获得零维和一维DB。前者位于两个空间维度上，而后者仅位于一个维度上。在一维DB中，考虑了两个族：第一个族基于三角晶格的DNVM，第二个族基于链的DNVM。我们推测我们对三角形的系统方法$\beta$-FPUT晶格揭示了所有可能类型的空间局部振荡，其频率从声子带的上边缘分叉，因为分析了所有频率高于声子带的DNVM。