Optical Solitons in Presence of Kerr Dispersion and Self-Frequency Shift

Abstract

We consider the higher order nonlinear Schr\"odinger (HNLS) equation describing nonlinear wave propagation in light guides with all higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. Using the Painlev\'e analysis, we derive all parametric conditions for soliton-type pulse propagation in HNLS fiber system. We generalize the Ablowitz-Kaup-Newell-Segur method to the $3\ifmmode\times\else\texttimes\fi{}3$ eigenvalue problem, and constructed the Lax pair for the integrable case. The one soliton solution is generated from a B\"acklund transformation and an exact N-soliton solution is explicitly obtained from the Hirota bilinearization. The significance of the soliton solution is discussed.