Discrete breathers are spatially localized periodic solutions in nonlinear lattices. We prove the existence of odd symmetric, even symmetric, and multi-pulse discrete breathers in strong localization regime in one-dimensional infinite Fermi-Pasta-Ulam lattices with even interaction potentials. The multi-pulse discrete breather consists of an arbitrary number of the odd-like and/or even-like primary discrete breathers located separately on the lattice. The proof applies to both cases of pure attractive and repulsive-attractive interaction potentials.

中文翻译：

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无限费米-帕斯塔-乌拉姆晶格中奇数、偶数和多脉冲离散呼吸器的存在

离散呼吸器是非线性晶格中空间局部化的周期解。我们证明了奇对称、偶对称和多脉冲离散呼吸器在具有偶相互作用势的一维无限 Fermi-Pasta-Ulam 晶格中的强定位状态中的存在。多脉冲离散呼吸器由任意数量的奇数类和/或偶数类初级离散呼吸器组成，它们分别位于晶格上。该证明适用于纯吸引力和排斥吸引力相互作用势的两种情况。