  We consider a two-dimensional (2D) nonlinear Schrodinger equation with
self-focusing nonlinearity and a quasi-1D double-channel potential, i.e., a
straightforward 2D extension of the well-known double-well potential. The model
may be realized in terms of nonlinear optics and Bose-Einstein condensates. The
variational approximation (VA) predicts a bifurcation breaking the symmetry of
2D solitons trapped in the double channel, the bifurcation being of the
subcritical type. The predictions of the VA are confirmed by numerical
simulations. The work presents the first example of the spontaneous symmetry
breaking (SSB) of 2D solitons in any dual-core system.
