Study On The Dynamics Of Nonautonomous Strange Wave In Fiber Under Nonlinear High Order Effect

Rogue waves are usually refer to large-amplitude water waves appearing surprisingly in the ocean. They brings people a lot of disasters due to their unpredictability and powerful strength. Recent studies suggest that the formation of rogue waves can be explained by the nonlinear mechanism. Particularly, the rational solution of nonlinear Schrodinger equation, found by Peregrine in 1983, affords an official prototypical description of rogue waves. In fact, rogue waves not only exist in the ocean, but also in the atmosphere, superfluids, plasmas, ultra-cold atom system, and even nonlinear fiber system. In nonlinear fiber system, there have been phase and intensity modulation techniques, which make the system be a good platform to study dynamics of rogue wave conveniently. Optical rogue waves were excited experimentally and named by Solli in 2007. Inspired by the experiment, many works have been done based on rational solution of the nonlinear Schrodinger equation. In fact, there exists higher-order effects in nonlinear optics which can’t be ignored. The dynamics equation should be extended to include these high-order effects. The dynamics of rogue waves in presence of higher-order effects has been studied, but quintic nonlinearity is seldom considered. However, when increasing the light intensity in order to get shorter pulse, quintic nonlinearity becomes very important. Kundu-Eckhaus (KE) equation can be used to describe evolution of optical field in a nonlinear optical fiber with quintic nonlinearity and nonlinear dispersion effects. Considering that the system coefficients can be varied with propagation distance, we intend to study dynamics of rogue wave based on a generalized nonautonomous KE model.In this thesis, we present the rational solution of the generalized nonautonomous KE equation analytically. It is shown that rogue waves can exist in the system. We find rogue wave of KE is similar to the well-known NLS rogue wave under constant coefficient management. But their phase distributions are distinctive. For examples, we discuss dynamics of rogue wave under two different coefficient-management ways. Under exponential nonlinearity management, rogue waves’ peak decreases slowly and its trajectory has a twist. It shows that the peak, valleys, width and trajectories of the rogue waves have periodic behaviors under periodic nonlinearity management. We find the trajectories of the peak and valleys always maintain "X"-shaped structures. The higher-order effects just make the trajectories have a deflection and the deflection angle is determined by the strength of higher-order effects.