A detailed mathematical analysis is undertaken of solitary wave solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with (2) nonlinearity. The so called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter ff which includes both wave and material properties. Using variational methods, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive ff. Recently bound states (multi-pulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be ff 2 (0; 1) and the bifurcations occuring at the two extremes of this interval are uncovered
