Bistable guided solitons in the cubic - Quintic medium

We consider spatial solitons in a channel waveguide with uniform cubic-quintic nonlinearity. By means of the variational approximation and numerical methods, two branches of the soliton solutions are found, which are in contrast to their free-space counterparts; the bistability occurs exactly at those values of the propagation constant where the free-space solitons do not exist. The Vakhitov-Kolokolov criterion formally predicts that one branch should be unstable; however, direct numerical tests disprove this expectation, showing that all the solitons are completely stable. Besides the bistability, another feature of the solitons which is promising for applications is that their edges can be made much sharper than in the free-space solitons. Systematic simulations of the evolution of an initial Gaussian beam are also performed, showing that it quickly self-traps into a soliton of either type, or into a breather, but never decays into radiation.