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Strong numerical evidence is presented for the existence of a continuousfamily of time-periodic solutions with ``weak'' spatial localization of thespherically symmetric non-linear Klein-Gordon equation in 3+1 dimensions. Thesesolutions are ``weakly'' localized in space in that they have slowly decayingoscillatory 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 theoscillon states can be quantitatively described by the weakly localizedquasi-breathers.It is found that the quasi-breathers and their oscilloncounterparts exist for a whole continuum of frequencies.Comment: 33 pages, 34 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Oscillons and quasibreathers in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>Klein-Gordon model

Oscillons and quasibreathers in theϕ4Klein-Gordon model