  We consider soliton solutions of a two-dimensional nonlinear system with the
self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic
potential as an example. We investigate a single soliton in detail and find
criterion for possible collapse. This information is then used to investigate
the dynamics of the two soliton collision. In this dynamics we identify three
regimes according to the relation between nonlinear interaction and the
excitation energy: elastic collision, excitation and collapse regime. We show
that surprisingly accurate predictions can be obtained from variational
analysis.
