Cylindrical Pulsons in Nonlinear Relativistic Wave Equations

Numerical results to the Higgs scalar equation and the sine-Gordon equation with cylindrical symmetry are reported. Two separated energy regions are found where a Higgs kink develops into pulsons when reaching the origin r = 0, while only for higher energies a reflection is observed. The pulsons to both equations are studied in detail by modifying the initial kink shapes. In comparison with the spherical pulsons the cylindrical ones are extremely long-lived. For amplitudes slightly below half the distance between two (neighboured) vacua of the theories no decrease of the amplitudes and no perceivable radiation have been obtained by the numerical solution, examined during a time of order 1000. On the other hand, "heavy" sine-Gordon pulsons (with amplitudes 3π ∼ 4π) are found to decay fast during a time t ≈ 100 in cylindrical symmetry.