Nonlinear wavefields in optical fibers with finite time response and amplification effects

A higher order nonlinear integro-differential equation of the Schrِdinger type modeling the evolution of finite amplitude wavepackets in the presence of optical amplification and finite material- and polarization time responses is analyzed with respect to the dynamical evolution of localized solutions. Nonexistence of localized travelling and stationary wave solutions is pointed out for certain parameter regimes. Finally the linear stage of the modulational instability of plane waves is studied and it is shown that the finite time responses produce finite bandwidth instabilities.