Compact bright pulse and ultrashort-pulse in the nonlinear Kerr-like media

The extended nonlinear Schrödinger equation describing the propagation of light beam in the weak nonlocal nonlinear media in general, and in the optical fibers with nearly instantaneous nonlinear response of the medium in particular, is investigated. In the zero-dispersion limit, we show that the system exhibits stable stationary compact bright pulse with an arbitrary nonlinear phase-shift both for the focusing and the defocusing media. However, in the presence of the large linear dispersion, this compact pulse become unstable and may be either disintegrate or transform into the ultrashort bright pulse according to whether the system operates in the normal or in the anomalous region. The exact analytical expressions of these two pulses are derived and the results checked through numerical simulations.