Bistable-soliton pulse propagation: Stability aspects

Abstract

Making use of numerical collision simulations, we have examined the stability of the bistable solitary-wave solutions (predicted earlier by Kaplan [Phys. Rev. Lett. 55, 1291 (1985) and IEEE J. Quant. Electron. QE-21, 1538 (1985)]) to the generalized nonlinear Schr\"odinger equation for a wide range of nonlinear functions f(I), I being the intensity. Gradations of stability have been observed, ranging from absolute instability through ``weak'' solitons to ``robust'' solitons. For all models studied, it was found that dP/d\ensuremath{\delta}\ifmmode\bar\else\textasciimacron\fi{}<0 guarantees unconditional instability while dP/d\ensuremath{\delta}\ifmmode\bar\else\textasciimacron\fi{}>0 is a necessary condition for the existence of weak and robust solitons. Here P is the energy of the solitary pulse and \ensuremath{\delta}\ifmmode\bar\else\textasciimacron\fi{} is a propagation parameter. Sufficiency conditions for robustness of the soliton have also been suggested. We have further demonstrated that it is possible to construct physically realistic nonlinear models f(I) for which robust bistable solitons exist.