In this work we study a coupled differential equations system, which describes the propagation of a wave packet, composed of two waves with frequencies omega<FONT FACE=Symbol>0</font> (fundamental wave) and 2omega<FONT FACE=Symbol>0</font> (second-harmonic wave), in a quadratic nonlinear dieletric waveguide. Asymptotically, we show that these equations reduce to the nonlinear Schr¨odinger equation (NLSE). Solving the coupled differential equations system, we obtain soliton solutions for the time evolution of the packet in the dielectric waveguide. Finally, we discuss the property of soliton solutions, in particular the necessary conditions for their existence.
