Research On The Wave Management In Plane Waveguide

In this paper, we mainly study on the dynamics of rogue wave in a planar waveguide from the analytical solutions, and the analytical solutions of the related nonlinear Shrodinger equations are presented by similarity transformation theory. Specifically, the rogue wave solutions of a variable coefficient nonlinear Shrodinger equation which we need to solve can be given from the rogue waves of constant coefficient nonlinear Shrodinger equation by a transformation which maps the variable coefficient nonlinear equation into the fundamental equation. Specific, we make the soulution of constant coefficient nonlinear Shrodinger equation be a seed solution of the eqution. Next, we get the analytical solution of the variable coefficient nonlinear Shrodinger equation. Then, We has made the corresponding figure of rogue wave’s evolution by Mathematica. At last, We study the dynamics of rogue wave in a graded-index planar waveguide with oscillating refractive index.We find that an additional refractive index can be used to manipulate the trajectory of the rogue wave without changing its shape evolution characters. The density distribution profile of rogue wave with the highest peak can be kept well through manipulating the graded-index term and nonlinear coefficient. The peak is a constant. It is very different from the Peregrine rogue wave. Adding the gain or loss term, which only changes the peak of rogue wave. Furthermore, the trajectories of these nonautonomous rogue waves still look like an "X" shape. These results provide possibilities to manipulate rogue wave in nonautonomous nonlinear systems.