Soliton-antisoliton annihilation in 1+1 dimensions: Time-dependent Hartree approach

The nonlinear dynamics of soliton-antisoliton annihilation in 1+1 dimensions is studied in the mean-field approximation. Self-consistent equations of motion for the time-dependent Hartree state are derived from the variational principle, and the relationship to the classical equation of motion is shown. The method is applied to kink-antikink annihilation in 4 theory. It is found that a long-lived oscillatory state is formed after the collision. This is explained in terms of quasibound states of the mean-field potential, which decay through nonlinear terms in the interaction, producing narrow peaks in the spectrum of the emitted meson radiation.