  Quasi-breathers (QB) are time-periodic solutions with weak spatial
localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006).
QB's provide a simple description of oscillons (very long-living spatially
localized time dependent solutions). The small amplitude limit of QB's is
worked out in a large class of scalar theories with a general self-interaction
potential, in $D$ spatial dimensions. It is shown that the problem of small
amplitude QB's is reduced to a universal elliptic partial differential
equation. It is also found that there is the critical dimension, $D_{crit}=4$,
above which no small amplitude QB's exist. The QB's obtained this way are shown
to provide very good initial data for oscillons. Thus these QB's provide the
solution of the complicated, nonlinear time dependent problem of small
amplitude oscillons in scalar theories.
