发表机构
Institute for Analysis, Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院分析研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过鞍点方法与集中紧性论证，证明了非线性格点波动方程（含Klein-Gordon和FPUT格点）中怪波与呼吸子的存在性，其关键设计是引入非恒定系数使谱间隙充分打开。
AI 中文摘要
我们证明了非线性格点波动方程中怪波和呼吸子的存在性，这些方程包括非线性Klein-Gordon方程和FPUT格点（带有附加的局部力）。我们格点波动方程的主要特征是动力学部分$\frac{\mathrm{d}^2}{\mathrm{d}t^2}$乘以一个非常数函数$\frac{1}{d(t)}$，使得$\frac{1}{d(t)}\frac{\mathrm{d}^2}{\mathrm{d}t^2}$的谱中的间隙充分打开，以包含空间线性算子的谱。我们通过鞍点方法结合集中紧性论证，将解视为一个不定泛函的临界点。在时间$T$-周期系数的情况下，在与怪波相同的假设下，相同的变分方法也提供了呼吸子解的存在性，其时间周期是$T$的任意给定整数倍。
英文摘要
We prove the existence of rogue waves and breathers in nonlinear lattice wave equations including the nonlinear Klein--Gordon and the FPUT lattice (with added local forces). The main feature of our lattice wave equation is that the kinetic part $\frac{\mathrm{d}^2}{\mathrm{d}t^2}$ is multiplied by a non-constant function $\frac{1}{d(t)}$ such that gaps in the spectrum of $\frac{1}{d(t)}\frac{\mathrm{d}^2}{\mathrm{d}t^2}$ open wide enough to include the spectrum of the spatial linear operator. We find solutions as critical points of an indefinite functional using a saddle-point method combined with concentration-compactness arguments. In case of temporally $T$-periodic coefficients and under identical assumptions as for rogue waves, the same variational method also provides existence of breather solutions whose temporal period is an arbitrary prescribed integer multiple of $T$.
