Abstract
We give the exact bright solitary wave solutions of (2+1)-dimensional nonlinear Schrödinger equation and analyze the effects of group-velocity dispersion (GVD) on the self-trapped pulses in a planar waveguide. The results show that the self-trapped pulses are unstable and collapse at higher peak power in a planar waveguide with the anomalous GVD, but the collapse does not occur in a planar waveguide with the normal GVD; the peak power required for self-trapping of the pulse in a planar waveguide with the normal GVD is less than the critical peak power for collapse of the pulses in a planar waveguide with the anomalous GVD.