Embedded solitons: a new type of solitary wave

We describe a novel class of solitary waves in second-harmonic-generation m odels with competing quadratic and cubic nonlinearities. These solitary wav es exist at a discrete set of values of the propagation constants, being em bedded inside the continuous spectrum of the linear system ("embedded solit ons", ES). They are found numerically and, in a reduced model, in an exact analytical form too. We prove analytically and verify by direct simulations that the fundamental (single-humped) ESs are linearly stable, but are subj ect to a weak nonlinear one-sided instability. In some cases, the nonlinear instability is so weak that ES is a virtually stable object. Multi-humped embedded solitons are found too, all being linearly (strongly) unstable. (C ) 2001 Published by Elsevier Science B.V. on behalf of IMACS.