‘‘Robust’’ bistable solitons of the highly nonlinear Schrödinger equation

We found that for some highly nonlinear Schr\"odinger equations (as contrasted to the cubic equation) the criteria of stability of solitary waves against small and large perturbations do not coincide, which results in the existence of ``weak'' and ``robust'' solitons, respectively. We have shown that bistable solitons, predicted earlier by Kaplan, are robust for some particular nonlinearities and, therefore, physically feasible. We have also suggested a general criterion for robustness of solitons.