Many dimensional U(1) solitons, their interactions, resonances and bound states

Head-on collisions of two-space dimensional U(1) solitons have been studied via computer in the framework of the Lorentz-invariant Klein-Gordon equation with a logarithmic non-linearity. Four different regions of parameters of the system ('charge' and velocity) have been found: (1) quasi-elastic soliton interaction (2) post collisional decay of solitons (3) decay of solitons during resonance (4) bound (oscillating) states of solitons. The second and the third types of phenomena have been found for the first time and have no analog in one space, one time dimension world. (Auth.)