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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.
We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have a strictly finite size. They do not emit radiation.
Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with nonlinear term of the form sign(phi) are presented. They are constructed from cubic polynomials in the scale invariant variable t/r. One class of solu
The regularized signum-Gordon potential has a smooth minimum and is linear in the modulus of the field value for higher amplitudes. The Q-ball solutions in this model are investigated. Their existence for charges large enough is demonstrated. In thre
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
We study the decay of large amplitude, almost periodic breather-like states in a deformed sine-Gordon model in one spatial dimension. We discover that these objects decay in a staggered fashion via a series of transitions, during which higher harmoni