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 Athe (2+D-dimensional and concentrate basically on the question as to Awhether there exists a stable, self-trapped solution. The positive Aanswer is obtained within the variational and the numerical method. ANamely, it is observed that neither spreading nor catastrophic Aself-focusing can develop and an oscillating, self-trapped solution arises. Numerical results show, in contradiction to the variational Aones, that am- plitudes of those oscillations decrease with Apropagation distance and for sufficiently large distances they vanish Ato zero.