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

This paper studies a discrete one-dimensional monatomicKlein--Gordon chain with only quartic nearest-neighbor interactions,in which the compact-like discrete breathers can be explicitlyconstructed by an exact separation of their time and spacedependence. Introducing the trying method, it proves thatcompact-like discrete breathers exist in this nonlinear system. Italso discusses the linear stability of the compact-like discretebreathers, when the coefficient ($beta$) of quartic on-sitepotential and the coupling constant ($K_4$) of quartic interactivepotential satisfy the given conditions, they are linearly stable.