Soliton-antisoliton scattering and capture in λφ4 theory

In this work we have investigated the result of collisions of a soliton-antisoliton pair for various incident velocities in λφ⁴ theory through a series of numerical experiments. It is observed for incident velocities less than a critical velocity V_crit that we have two narrow regions in the velocity spectrum where the result of collision is a scattering of particles along with the emission of some radiation. Outside these two narrow windows the incident particles are captured and form resonances. For velocities greater than V_crit scattering is always obtained and it is found that the square of the outcoming velocity is a linear function of the square of the incoming velocity. From the approximate solution found, an effective potential for widely separated solitons is derived.