Oscillons and Quasi-breathers in the φ⁴ Klein-Gordon model

Strong numerical evidence is presented for the existence of a continuous family of time-periodic solutions with ``weak'' spatial localization of the spherically symmetric non-linear Klein-Gordon equation in 3+1 dimensions. These solutions are ``weakly'' localized in space in that they have slowly decaying oscillatory tails and can be interpreted as localized standing waves (quasi-breathers). By a detailed analysis of long-lived metastable states (oscillons) formed during the time evolution it is demonstrated that the oscillon states can be quantitatively described by the weakly localized quasi-breathers.It is found that the quasi-breathers and their oscillon counterparts exist for a whole continuum of frequencies.