Bistable bright solitons in dispersive media with a linear and quadratic intensity-dependent refraction index change

Abstract

An exact analytical bistable (or two-state) soliton solution of the generalized nonlinear Schrödinger equation has been found for a medium with a linear and quadratic intensity depending refraction index change of the form δ n = n 2| A| 2+ n 4| A| 4. It is shown that for negative nonlinear coefficients n 2 n 4<0 and k'' L n 2<0 two possible soliton states exist, which describe undistorted pulses with the same duration but different peak power. It is proven that both solution branches are stable against small fluctuations.