论文标题
离散非线性klein-gordon晶格的定期行驶波解决方案
Periodic travelling wave solutions of discrete nonlinear Klein-Gordon lattices
论文作者
论文摘要
我们证明了一般离散非线性klein-gordon系统的周期性行驶波解决方案的存在，考虑到硬性和软现场电位的情况。在艰难的现场电位的情况下，我们实施了固定点理论方法，将Schauder的固定点定理与收缩映射原理相结合。这种方法使我们能够在能量空间中识别出存在非平凡溶液的环，其存在的能量（规范）阈值以及其速度上的上限。在柔软的现场电位的情况下，基于山间通过定理的变异方法促进了周期性行驶波解决方案的证明。还得出了这些解决方案的平均动能阈值。
We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point theory approach, combining Schauder's fixed point theorem and the contraction mapping principle. This approach enables us to identify a ring in the energy space for non-trivial solutions to exist, energy (norm) thresholds for their existence and upper bounds on their velocity. In the case of soft on-site potentials, the proof of existence of periodic travelling wave solutions is facilitated by a variational approach based on the Mountain Pass Theorem. Thresholds on the averaged kinetic energy for these solutions to exist are also derived.
