The generalized nonlinear Schrödinger equation with certain nonlinearities allows for 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 of them exhibit either “weak” stability (i.e. stability against small perturbation) or absolute stability (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 non-linear optics, these solitons may exist either in the form of short bistable pulses, or bistable self-trapping (both two- and three-dimensional).