Are there soliton-like solutions of coupled (1+1)- and (2+1)-dim NSE?

We consider two coupled nonlinear Schrodinger equations, the (1+1) and the (2+1)-dimensional and concentrate basically on the question as to whether t here exists a stable, self-trapped solution. The positive answer is obtaine d within the variational and the numerical method. Namely, it is observed t hat neither spreading nor catastrophic self-focusing can develop and an osc illating, self-trapped solution arises. Numerical results show, in contradi ction to the variational ones, that amplitudes of those oscillations decrea se with propagation distance and for sufficiently large distances they vani sh to zero.