We investigate the stability of bright solitary waves formed by the mutual trapping of the fundamental and second-harmonic waves propagating in a nonlinear quadratic medium. First, we find that most of the solitary waves are stable under propagation. Second, we study the evolution of the solitary waves in the presence of small linear absorption. At phase matching the adiabatic evolution of the solitary waves obeys an amplitude × width-squared rule.
Torner, L., Mihalache, D., Mazilu, D., Amhmediev, N. Stability of spatial solitary waves in quadratic media. "Optics letters", Novembre 1995, vol. 20, núm. 21, p. 2183-2185.