New features of soliton dynamics in 2+1 dimensions

Exponentially localized soliton solutions have been found recently for all the equations of the hierarchy related to the Zakharov-Shabat hyperbolic spectral problem in the plane. In particular theN²-soliton solution of the Davey-Stewartson I equation is considered. It is shown that the boundaries fix the kinematics of solitons, while the dynamics of their mutual interaction is determined by the chosen initial condition. The interacting solitons can have, asymptotically, zero mass and can simulate quantum effects as inelastic scattering, fusion and fission, creation and annihilation.Work supported in part by M.U.R.S.T.