BISTABLE OPTICAL SOLITONS

Abstract
The generalized nonlinear Schrödinger equation with certain nonlinearities allows for the existence of multi-stable single solitons (i.e., singular solitons with the same carried power but different profiles and propagation parameters). Some of these new solitons are absolutely unstable, whereas the rest fall into two classes of either "weekly" (i.e. stable against small perturbation) or absolutely stable solitons (the so called "robust" solitons that are stable against arbitrary perturbation, in particularly in the form of collision with another large soliton). The criteria for both weak stability and robustness are suggested and tested in computer simulations for various models of nonlinearity. In nonlinear optics, these solitons may exist either in the form of short bistable pulses, or bistable self-trapping (both two- and three-dimensional). The recent research shows that the bistable solitons can be switched from one stable branch to another and that the originating nonlinear equation passes the Painleve test for complete integratibility.