Swaying oscillons in the signum-Gordon model
  We present a new class of oscillons in the (1+1)-dimensional signum-Gordon model. The oscillons periodically move to and fro in the space. They have finite total energy, finite size, and are strictly periodic in time. The corresponding solutions of the scalar field equation are explicitly constructed from the second order polynomials in the time and position coordinates. 
H. Arodz and Z. Swierczynski
hep-th math-ph math.MP nlin.SI