The investigation of solitary waves due to cascading has become one of the most interesting topics of nonlinear optics. Unfortunately the resulting system of two complex nonlinear equations seems do be not integrable. In the limit of infinite phase mismatch or pulse width the equations can be reduced to the NLS which is integrable and where solitons are known. But this special limit corresponds to diverging pulse energies required. Therefore a detailed analysis of the initial equations is unavoidable. It is known that in the stationary limit the equations have some bright solitary wave solutions, which have to be determined numerically except of one where an analytical form is known. Some of those solutions are stable during propagation some are not. We study the propagation and fusion of those spatial solitary waves in a quadratic nonlinear medium numerically. If we neglect the so-called walk off we can make use of the Galilean invariance of the resulting equations and can construct moving solutions from stationary ones. This method seems to be the best to test whether the solitary waves found are true solitons. We find that if the solitary waves collide with a high relative velocity they penetrate each other and therefore behave like real solitons. If one undergoes a critical velocity both solitary waves merge and form a new stable but oscillating state while some energy is lost by radiation. Even near the Schr\"odinger limit (big phase mismatch) the collision behaviour differs from that found for the solitons of the NLS. Further the final state critically depends on the phase difference between the initial solitary waves. Phase differences generally reduce the probability of a fusion but may cause some energy exchange between the different solitary waves.