Studies On Transmission Properties Of Optical Solitary Waves Under The Higher-order Effects

Starting from the higher order nonlinear schroedinger (HNLS) equation, we investigate the propagation characteristics of ultrashort optical pulses in optical fibers from the analytic point of view. What we discussed in this paper may improve the analytic foundation for realizing the transmission of fast-speed and high-capacity optical information systems. The main results are as follows:1) By using AKNS formalism we construct the Lax pair for Hirota equation, a higher order nonlinear schroedinger (HNLS) equation. And based on the Lax pair, we present exact N-soliton solution by employing simple, straightforward Darboux transformation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically.2) Under the nonvanishing boundary, we solve the Hirota equation by using Darboux transformation. The exact analytic solutions (a) modulation instability (MI) and (b) soliton propagation on a continuous wave background have been given. In addition, we analyze the amplification absorption and quintic nonlinearity effects on the second solution in the adiabatic approximation.3) We consider the averaged dispersion-managed (DM) fiber system equation, which governs the dynamics of the core of the DM solitons. For a special case of such a system equation, we derive the exact soliton solutions using the Darboux transformation. Further, we discuss the interaction scenario between neighboring solitons under the influences of chirp effects.