Compact-like discrete breather and its stability in a discrete monatomic Klein--Gordon chain

This paper studies a discrete one-dimensional monatomic Klein--Gordon chain with only quartic nearest-neighbor interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient (\beta) of quartic on-site potential and the coupling constant (K₄) of quartic interactive potential satisfy the given conditions, they are linearly stable.